Coming back to this to say that I think it depends on the main intake points of the 'next step' school you are looking at.
If the 'next step' school has its main intake at 11+, then School A would 'match' that, as it is the normal exit point [and cynically, they won't miss out on any fees], and one that they will gear e.g. their curriculum, test preparation etc towards.
If on the other hand, the main intake of your preferred 'next step' school is at 7 or 8, it is possible that School A might be less 'unequivocally helpful and ambitious' in preparing for it, as you are taking a child away from them mid-career. In such a case, School B + tutoring might be a better way forward.
Some relatives had this experience they entered a child into a 'to 11' private school, intending to transfer to a 'big name' prep at 7+. as the school didn't particularly WANT children leaving at 7+, the amount of support in 7+ choice / preparation was very limited, and the child failed. Roll forward to 11+, the school threw everything at exam prep for several terms, and the child managed to get into the same prep as an 11+ entrant, because there is a significant intake then. Had the 7+ intake been the 'main entry point', with 11+ only being minor and for exceptional / state educated children, I suspect that this child would have failed then again.