So your user journey is:
click Google Ads ad --> open landing page on 1st domain --> click a link --> open landing page on 2nd domain --> fill up form --> submit form (conversion)
I assume that you're tracking the 2nd domain to the same report suite as the 1st domain.
Are you already using cross-domain tracking to pass your visitor ID over from the 1st domain to the 2nd domain? If you are, then AA should be able to link the user journey properly between the 2 domains such that you don't need to pass the CID over as well.