Depends; Probably Yes
Memory is largely still a mystery to us. Current theories vary widely, and all lack sufficient scientific backing. I will focus on the theory of memory which I, personally, think is most likely to be true - although, again, memory is mostly a mystery to us.
The theory I like the most is, basically, that thoughts are nothing more than patterns of neurons in our brains. Furthermore, a "memory" is simply that pattern of neurons firing, and "recalling" a memory would be that pattern firing again in your brain. As such memory is not a "thing" that is stored, which means it cannot be read or copied after the fact; the only way to "record" a memory would be to either (a) capture the thought as it occurs, or (b) have someone "recall" a memory, and capture that neural pathway as it happens.
In a futuristic setting, maybe we have learned more about how these neurons fire with one another, and can then create these memories on a computer, or something of the like.
Neither your question nor this answer address how this will occur. You reference a similar question where the answers say transmitting memories to others is "basically not possible" because of different brain structures. I have a slight disagreement with that - in a futuristic sci-fi setting, will we be able to reconfigure brain patterns? It's not so far-fetched as to be "impossible", and depending on how practical you want your story to be, I think this can be hand-waived some. If we can stimulate neurons to move around inside a brain, then we can place neurons in the right order so as to have - and fire - the memory pattern. Or maybe you scramble their brain to the point they can't function and fall over dead.
That said, some of the (well documented) cases of dreams or memories which occur from organ donors to their recipients tells me that how our bodies interact with the world, our organs, feelings, etc, allows for some memories to move if brains are similar enough. While brains may be 99% unique, if there is 1% in common, then some memories, feelings, etc, can be shared. Theoretically
If someone with amnesia - likely from a brain trauma - can't recall certain memories, that means their neurons have shifted around enough that the neural pathways aren't firing. Their brain is likely similar enough to be reminded / reordered to then recall some memories.
Given that people with amnesia do often regain their memory through natural means, I don't see any reason why a futuristic technology could exist to either aid in this recovery, or simply perform the recovery function through some invasive means.
In any case, the question becomes can the neurons be ordered in such a way that this specific pathway [memory] can be triggered? If so, then the answer is yes. Given that (a) this is the theory of memory that makes the most sense to me, albeit lacking scientifically, and (b) the amnesiac's brain is likely close enough for those patterns to be available, then I would say probably yes.
