He invites her into his heart almost immediately. He's open and unscarred, and he has the luxury of doing so without fear of getting hurt. She's the first one he has ever offered it to, but she subtly – and then, later, bluntly – makes excuses to avoid coming over. In time, he stops asking, but he never closes the door on the possibility of her.
It takes a while for her to trust and like him enough to invite him to visit her heart. By the time she does, all of the doors and cupboards are open for his use. She takes him on the grand tour, and he compliments its upkeep, genuinely impressed by her beating home. And, finally, he takes her back to his as well.
It isn't long until she gives him a spare key, offering him full use of the abode. He give her one for his as well; it has always been hers, too, after all, even if she has only just accepted it. They cherish the exchange, splitting their time between the two houses.
Soon thereafter, they agree to move in together officially, and they do so without any fanfare. They dig a tunnel to connect their hearts so that they can come and go as they please, just the two of them. It's theirs and theirs alone.
They have spent so much time at each place that it seems like the natural next step, after all. Their things and their lives seem to fit together perfectly, melding into one until her place is his and his place is hers and both places are theirs.
And there they live, forever, in one another's hearts.