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It's obviously possible since instinctive behavior is an easily verifiable scientific phenomenon in animals. So the real question is what memories(if any) are transferred from one generation to the next.

Inheriting specific memories like William T. Stead described in "Letters from Julia" isn't supported by science. Memories are formed through experiences and stored in the brain's complex network of connections. Since DNA doesn't hold those intricate details, they can't be passed down like eye color or height.

However, there are some interesting areas of ongoing research:

Epigenetics: This field explores how genes can be influenced by environmental factors. Maybe a parent's traumatic experience could leave an epigenetic mark that somehow affects their offspring's vulnerability to similar situations. It wouldn't be a direct memory, but a potential predisposition.

Collective Unconscious: This concept from psychology suggests a shared pool of memories or experiences across humanity. It's a more philosophical idea, but it could explain why some people have phobias or anxieties with no clear source in their own lives.

Overall, the science leans towards "no" for inheriting specific memories. But the field is constantly evolving, and these areas of research offer possibilities for how our ancestors' experiences might leave a subtle mark on us.