BOAC is right, I'd assume a buy out would be the simplest form. If the company you describe doesn't hold an AOC, this would mean they'd have to be audited and I assume would be a larger ordeal than a simple merger.
My knowledge as I said is limited (I'm not a quality department person) and wouldn't have any idea about how you could merge an AOC from a current holder to a new company without an AOC but I guess the non AOC company takes over, and as long as the current AOC holder remains in place (or there is a suitable replacement) and the fleet size and employee size doesn't change I would assume this would be fine as nothing changes in reality, just ownership.
Aka a paperwork exercise.