Hello, welcome to the website. My name isXXXXX can assist you with this.
If may be able to say that he had abandoned the property and left the tenancy. Factually, this seems to be right, as the girlfriend signs a new tenancy agreement and she continues to make the payments in her own right.
I believe you're entitled here to say that he has no rights, he abandoned the tenancy, and a new tenancy has now been granted to her, and that continues until she (or you) choose to end it.