Is repentance for all sins accepted, despite persistence in some of them and delaying general repentance?

According to the majority of scholars, repentance from a sin is valid even while persisting in another. However, such a penitent does not fully deserve the name of "true penitents" nor their complete virtue. It is advised to repent from all sins immediately. But if you repent from some sins while not from others, your repentance for what you repented from is valid if it fulfills the conditions (abandoning the sin, resolving not to return to it, and remorse).