# a closed projection on a C*-algebra is compact iff it is closed on the multiplier algebra

I'm trying to understand the proof for the equivalence of (i) and (v) in the following picture. I don't quite understand what the highlighted sentence means. I want to know why there is a surjection from $$B$$ onto $$M(A)/A$$. Can anyone explain for me, or provide some other proof? Thanks in advance.

The picture can be found in the following paper:

Brown, Lawrence G., Semicontinuity and multipliers of (C^*)-algebras, Can. J. Math. 40, No. 4, 865-988 (1988). ZBL0647.46044. 1: https://i.stack.imgur.com/v3UGY.png