Person A in an immortal being. Just like any other regular human - just that they can't die naturally.

Person B is just a regular human - but they are in love with Person A.  Person A is reluctant to be with them, knowing that they will have to live without Person B once they die. When Person B does die, Person A vows to find them in every life afterwards so they can be together. 

What happens when Person A finds Person B?