Applying to my first reference and using him as referee
If I understand correctly, Mr A. moved to another institution and you want to apply to a position at that institution under the same Mr A.

Your best course of action would be to contact Mr A. directly and tell him that you would love to apply for that position and ask him whether it is ok for you to include him as a reference. This would then of course be just a formality, as Mr A wouldn't write a reference to himself, but it would serve to fill out the field and to implicitly constitute a recommendation.

This is important as to counter any eventual conflict of interest. If Mr A can't be your reference, perhaps he can point you to others (this part of your question is a bit confusing).

There are institutions where students apply directly to the professors, if that is applicable here, Mr A could be more inclined to accept you.