HIV does not generally infect the germ cells that produce sperm or eggs, so it is not heritable, which is maybe the sense you interpreted OP's comment.
Still, HIV is a provirus. Retroviruses write themselves into the genome of the host cell. Cells which are infected and survive to reproduce carry the HIV provirus. As will their descendants, and so on. They will produce HIV when mature even without any HIV particles in the cell. This is integration with the host genome.
This is why HIV cannot be cured with antivirals which fully inhibit its replication. It's also why complete destruction of the immune system (in the process destroying all the cells which are the specific hosts) while flooding the body with high dose antivirals, and then grafting innately immune T-cells, is an effective, if rather drastic, cure.
Still, HIV is a provirus. Retroviruses write themselves into the genome of the host cell. Cells which are infected and survive to reproduce carry the HIV provirus. As will their descendants, and so on. They will produce HIV when mature even without any HIV particles in the cell. This is integration with the host genome.
This is why HIV cannot be cured with antivirals which fully inhibit its replication. It's also why complete destruction of the immune system (in the process destroying all the cells which are the specific hosts) while flooding the body with high dose antivirals, and then grafting innately immune T-cells, is an effective, if rather drastic, cure.