It would certainly be possible for a Psychic-type to share their trainer's memory with another person, however, this comes with two cravats.
First, this is not something that comes naturally to pokemon. It's very much like speaking -- it's something they are capable of, but it will require a lot of training to get there. And no pokemon would be capable of transmitting an entire memory at first. It would certainly be the kind of skill that slowly builds up over time, first starting with perhaps sharing a single mental image, to some impressions, to over time, a longer memory.
Second, and this ties in with the first thing, because it is so difficult for a pokemon to do this, even with training, it will only be something a pokemon can do to one other person at a time.
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First, this is not something that comes naturally to pokemon. It's very much like speaking -- it's something they are capable of, but it will require a lot of training to get there. And no pokemon would be capable of transmitting an entire memory at first. It would certainly be the kind of skill that slowly builds up over time, first starting with perhaps sharing a single mental image, to some impressions, to over time, a longer memory.
Second, and this ties in with the first thing, because it is so difficult for a pokemon to do this, even with training, it will only be something a pokemon can do to one other person at a time.