The IRS form 1099-B is reported to state A and you, correctly, report the income to state B.
State A has already received the notification of the IRS form 1099-B and will be expecting the income to be reported on a state income tax return.
At a later time, state A may contact you about why you did not report the income to that state.
Make sure that you retain paper records that fully explains your decision, should the tax authority of state A contact you at a later time.