There is only one way to lift a warrant, and that's for either your husband or a California lawyer working on his behalf to go back before the court which sentenced him 17 years ago and have the judge remove the warrant.
Unfortunately, however, a probation sentence is one that is given in place of a jail sentence. At the time your husband took the plea, he was instructed that if he did not finish his probation successfully, he could be resentenced to jail for the maximum amount of time the case is worth. So both the DA and the prosecutor are going to want the judge to resentence him to prison. This means if he goes to court in California to take care of the warrant, the judge would almost certainly put him in jail and set bail on him to hold him until the hearing on his 17-year old violation of probation.
Proposition 47 was not around 17 years ago. That's a special Act that reduces penalties for certain kinds of California drug crimes and that may be helpful to your husband, depending on the nature of his charges. He needs to talk to a California lawyer and find out whether this warrant can be lifted and his case resolved without his having to do any jail or prison time upon resentencing. Sometimes after 17 years the state might be lenient in the case of a person who has otherwise stayed out of further difficulty with the law for that time.
So, in short, the only way he can clean up his past is to go back to California and deal with his case. But he should let a California lawyer look into that so that if at all possible, the lawyer can pave the way for as safe a return as possible.
If he doesn't know where to find a California criminal lawyer, he can try the California Bar Association's Lawyer Referral Service.