Tatiana, both of the translations you suggested are exactly what I would say as a native. In fact, I added my translations before I read your comment))) Good work!

The other two translations are grammatical, but simply not something a native would say, for instance, when shown a photograph by a detective in a crime investigation or a missing person case.

He mentioned having seen him before.
He mentioned seeing him before.
В этом случае тоже оба варианта верны?

Вполне верны!

Thank you!)

You’re quite welcome)))