Acquiring memories and personalities through organ transplants is a somewhat known urban legend and a fiction trope, but AFAIK the only thing you can transmit through a transplant that's been verifiably demonstrated is pathogens.
https://www.nytimes.com/2019/12/07/us/dna-bone-marrow-transp...
Maybe not quite a 'long-term' memory in the context you're after, but I wonder how this would compare to something like instinct and how we would tell the difference?
Somewhat related to this is Microsoft Research's project to use DNA for data storage: https://www.microsoft.com/en-us/research/project/dna-storage...
Maybe a “memory” like a neuron based thing isnt what is being transmitted, but instead nearest urges directed by unique sets of microbes found in individuals