Sure it is possible. After all, what we term "natural instinct" would seem to be contained within the genetic code. It is not a far reach to consider the possibility that more individual memories might be encoded there also. Since we really don't understand how information like instinct is encoded there; it is difficult to see how individual memory could be encoded.
However, there are indications that more specific information than instinct is encoded in us. Witness the various cases of twins separated at birth and then reunited many years later. They both owned the same model of car, same breed of dog, their wives look similar, same work field, etc...
As to passing memories on to offspring; only memories prior to the production of the egg or sperm would be conveyed by the respective DNA. Some other means would have to be possible for later memories. A quantum process maybe?? Lots of possibilities have been explored in various novels such as the Dune series by Frank Herbert. In it, the Bene Gesserit sisterhood pass on memories from one to another by mind sharing. Another interesting idea is in Anne Rice's book, The Queen of the Damned, where the sisters belong to a tribe that ritually eat their dead so as to preserve/save their essence.
We are at the frontier of genetic knowledge and who knows what wonders lie over the horizon.
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