Only through a new petition. L-1B and L-1A are distinct classifications with distinct tests, so a move into management requires establishing that the duties are primarily managerial or executive on the new facts. Time already spent in L-1B counts toward the maximum period and is not reset by the change.
A title change is not a classification change
Companies frequently assume the classification follows the promotion, because internally it does. It does not for immigration purposes. The person was admitted on the basis that he holds specialised knowledge of the organisation's processes and will apply it; the managerial classification asks a different question entirely, about whether he will manage an organisation, department, subdivision or function, supervise supervisors or professionals, and hold authority over personnel and operations.
Both can be true of the same person, but each has to be proved on its own terms in its own filing. Two further consequences follow. First, the promotion should not take effect before the petition is filed and, depending on advice, approved, because in the interim the duties would not match the approval.
Second, the periods do not restart: prior L-1B time is generally counted toward the seven-year L-1A maximum, so a person promoted in year four is not beginning again at zero. That arithmetic should be done before the offer is made.