Should I change my financial advisor when moving to another state?

I'm moving permanently to Washington state this summer from California. I have both investment and IRA accounts managed by a local Wells Fargo financial advisor. He told me he can apply for a WA license to continue managing those accounts for me. However, I want to cut ties with California completely with my move to avoid any potential state taxes. Should I change my financial advisor when moving to another state? Would I have to pay any California tax(es) if I keep him with me? Thank you for your opinion.