tl;dr There are multiple problems about defining the various parts of this question (like what a proof means in this scenario) and how the claims of the being existing in both realities might be interpreted by a sceptical person. But my personal verdict would be you can get the other being to believe in the other reality but you cannot proof it.
(I hope this post is not too long but I was a bit interested in these kinds of questions for world building myself so my answers are a bit lengthy.)
I think the task of getting A to believe that reality X of B exists
gives C multiple different problems and as we are already talking
about different realities the solutions might in the end depend
heavily on properties of those realities and their inhabitants, that
are fundamentally different from our own or even your views on what
can be seen as a proof or what exactly needs to be proven.
There is the problem of how a physicist A would have to solve the task
in getting information about this other reality by proxy of C. But
there is also the problem of how a philosopher A would interpret it
and actually say the claim of C "there exists another reality from
this one" is true or false or any other claim of C about this other
reality of B for that matter because C wanted to prove not only
certain properties but the actual "structure" of the reality.
The problem with the philosopher A interacting and communicating with C
and interpreting the findings of physicist A is the following. When do
I say a "reality" "exists"? For example no matter what you tell me
about our actual universe with planet earth and everything I could
argue, that it is just made up in the back of my mind and none of the
persons I see really exist. But if I form the will in my head to stomp
my foot on the ground and my foot and leg move as if I had a foot and
a leg and they stomp on what looks like there is a ground that belongs
to the planet earth as if such a thing exists maybe you could say
reality exists but there is no actual proof of reality existing. There
is just the interpretation, that the things that I perceive are part
of a reality. This might sound like a non-issue for most of us but
depending on what kind of philosopher A is it might come to different
conclusions about these kind of claims especially because there
already is a reality that it calls its own so everything else is
either part of this reality anyway and is perceivable anyway or its
perception behaves as if it does not exist, so that might be important
if you think of A actually arguing with C about the reality of B.
I think what we should say is that this task of C to persuade A of
another reality can probably not solved by mere communication, because
all that would prove is that C talks to A as if there would be another
world for C to perceive but A would just tell C that it should stop
all this world-building in its head and get a real hobby.
But now to what would actually be the basis of all this philosophical
arguing about what might be non-sense or not. Physicist A has to start
its work and its object of interest is C. Now C has to be very
cooperative about all of this. Basically to get the best kind of
argument about the reality of B that A can only perceive "through" C A
has to analyze C in every conceivable way possible with the scientific
method.
The other answers speak about for example taking an object from the
other reality, but that would look to A only as if C can materialize
objects from thin air, which depending on the universe they live in
might be impressive or not but not a proof for a different reality
actually existing. Even if it would have properties that only things
in the other reality can have, A would not know that those properties
exist on the other reality. This would also have to be proven to A by
C. I guess you see the problem here, the properties would also just be
seen as being new in this world and created out of thin air, so there
still is no proof.
Now lets think about all the ways A could analyze C to figure stuff
out about the other reality of B. A could try to push C but if B stands
behind C and does not let C move A would be confused about that. If B
would heat up C so that energy seems to just come into existence
another thing about the laws of physics that A believed in might have
been just proven false. But A would as a physicist only think of those
things as things that it did not know before about its own reality and
it would think that C is a thing with special properties, but only in
this reality.
So the problem is, if A believes, that it can still figure out new
stuff about the world it will through C only find out more properties
about how C interacts with its own reality, everything as if C would
have its own rules but maybe not its own reality where there are
things like B that communicate with it in some way. Every form of
communication can just be seen as made up or popping into existence
from nowhere.
So A can use C to scan the other reality of B like a blind man scans
his surroundings with a stick, but the interpretation of its findings
might just be something scientifically sounding like:
"C reacts to some field that we cannot interact with directly, and
this field does not let C through as if the claim of C that there is
another person that I am trying to push C through is standing behind C
were true. And the field disappears sometimes as if the claim of C
that the person has gone away were true. But we cannot catch that
person that C is talking about because nothing in our reality except C
interacts with it, so the thing does not really act like a person,
more like a magical field, that sometimes pops up and sometimes goes
away, with some other rules i could find out about it that make its
behavior somewhat predictable. I will call this field the dark field
(because we can only perceive it indirectly like dark matter) and get
a nobel price for the weird properties I have found out about C and
some field that interacts with C. Maybe we will figure out more stuff
about that in the future"
So C cannot prove A that anything that is able to communicate with him
exists in a different reality, and for everything that does happen
with C in the other reality, A might interpret it in the simplest way
possible like "it just appeared out of thin air" but not like "it
appeared, so it must belong to a different reality and the people C is
talking to are real".
But A could also just call that a different world "the world of C" or
something like that. Or A could just stop being a sceptic and just
believe in the claims C is making as we do all the time in the "real"
world with our believes, but there would never be absolute proof for a
being communicating with C because even if as in a different answer
two things of the type of C would know something because B helped
would probably be interpreted as a direct form of communication
between the to C-like things but not as something like B being
here. That might just be the interpretation of C of what is happening
because C is hallucinating.
However if for some reason A knows with absolute certainty that some
things just are not possible in its world, because maybe A created
this reality and knows everything about it and its consistent logic,
then that axiomatic truth might be used to deduce that something
different must exist. But as far as I know at least we as humans have
no proof of anything existing at all we just take this fact as given
because it seems obvious.
So either A needs special information, that we cannot have or C needs
to be able to basically bullshit A into believing its lies. At least
other people in the reality of A would not know the difference between
the other reality existing or A just being really gullible and C
making stuff up.
But this is a weird topic to think about. I guess because of the
nature of thinking about alternate realities a lot of this stuff
depends on how something would be interpreted philosophically or what
type of assumption you could make about the basic logic of different
realities. So you maybe had to define what the consciousness of a
different being is and how it works together with things that are
objectively perceivable and maybe you could prove the existence of
communication with a different being that nobody else can
perceive. Although I myself would not be THAT sceptical if you would
only want to prove to me that somebody on the other side of the world
exists and we can communicate with that over the Internet with a
computer. So maybe talking about what a REAL proof is might be a bit
unnecessary. I believe things, that I have no REAL ABSOLUTE proof for
all the time. The medias I consume ARE my reality, if the things they
talk about exist or not and I behave as if those things exist, even if
the maybe don't. Maybe C would say that is proof enough, that I
believe in them and C should focus on making A behave as if the other
reality is existing. If A would have an incentive to believe the
claims of C, then A and maybe all other beings would act like that,
but now we are debating as what counts as "proof" if there is no other
absolute proof.
So to wrap up, there would through the scientific method and logical
deduction in a reality with the same logical rules as ours be no way
to absolutely proof the structure of the universe with two realities
existing and beings with consciousnesses and the ability to
communicate in both realities.
But I tried to include some possibilities for "alternative facts" in
other realities and some alternative ways of interpreting the claims
of somebody as "truth" then the scientific method and logical
deduction. I hope this helps and I did not go way too overboard with
my explanations.