I have a general question regarding mail routing.
I have two sites with a mail server and a different domain at each site. Site A is @toto.com and site B is @titi.com. Site A is also hosting a common domain which is @abab.com

I need to send emails to Site B which will send it to Site A.
So imagine user john with john.john@xyz.com needs to send an email to bob.bob@abab.com without knowing if bob.bob is a site A or site B user.
john.john sends an email like this:

from: john.john@xyz.com
to: bob.bob@abab.com

The mail server at site A receives it and after a lookup in the entry directory finds out that bob.bob is a member of site B. It then sends the following email to Site B mail server.

X-Apparently-To: bob.bob@titi.com
from: john.john@xyz.com
to: bob.bob@abab.com

but bob.bob would like to answer with its bob.bob@abab.com address, how does he do that? How does mail server at site B knows that it should forward the email to site A web server in order to have the email forwarded with the address bob.bob@abab.com? I have no clue.