I have seen numerous theories about Mars and Earth history presented separately. Rarely, if ever, do I see credible sources try to tie the theories/events together, even though the time frames are roughly the same. Perhaps the missing planet (or a large portion of it) struck the Earth and coalesced into what we now know, billions of years later, as Earth and Moon.
That hypothesis is currently popular. It was also the main hypothesis they taught us in grammar school in the 50s.