I decided to build upon PcMan´s awnser by trying to simulate this scenario using my (not all that accurate, but hopefully good enough for this) gravitational simulator. So i tried placing a 3x earth mass planet at earths L5 point and let physics do its thing. (My simulator could not handle having the moon in this aswell as the earth-moon distance is too small, but i suspect the moon to be rather stable during all of this as it sits rather deep in earths gravity well)
The result is that the lagrange points themselvs are utterly unstable, although what happend instead was that earth and this planet ended up in a horseshoe configuration with about 500 years as half-period. So what that means is that as the 2 planets are in slightly different orbits they end up with slightly different orbital periods(lets say that earth ends up with a shorter period), so then earth would slowly catch up to the other planet from behind and get sped up abit by the other planets gravity. At the same time the other planet would get slowed down a little as earths gravity pulls it backwards a tiny bit. This has the effect that the earth gets pulled into a higher orbit with longer period and starts falling behind the other planet, so they separate again. And then 500 years later earth has wrapped around the sun and starts approaching the planet from the front instead, and the same reversing process happens again and so on.
This means that as earth is on the inner,faster orbit the year would be about half a day shorter and when on the outer,slower orbit the year would be about half a day longer. Also note that all this orbital swapping has a tendency to give earths orbit higher eccentricity and that might mess with seasonal stability and the global climate.
This configuration is somewhat stable, atleast in the short-term. In my simulations it lasted about a million years or so but after that some rather nasty overlaps and resonances started happening and then a rather sudden disintigration of the whole setup, where in one case earth crashed into the sun. Ouch!
In these animations earth is represented by the green dot and the other planet by the orange dot. (i dont know how to get the gif to embed, sorry...)
This first animation shows the horseshoe orbit as it looks at the start(after it has settled down abit)
And this second one shows the instability at about 1.1 million years
So in summary: Placing this planet in earths orbit will work for about a million years but not more than that, so if the aliens want to stay for longer than that some kind of more permanent location will have to be found. But that seems abit out of topic for this question.
Or just do some good-fashioned stationkeeping using whatever magic brought their planet here to start with, as predicting and preventing this kind of instability is very easy compared to moving a whole planet between star systems. (The prediction part is something we humans can pretty much already do btw) Just give either or both of the planets a tiny nudge in the right direction every hundred years or so and this setup can last for aslong as you want it to.