Old Question (probably already answered) about Black and wands

[marephraim]

No: HPFGUIDX 112724

My daughter is reading POA for the upteenth time and asked me this 
question. In chapter 19 it says, "gowled Black, his own wand 
pointing at Pettigrew, too..." 

>From where did he get "his own wand"?

I opined that perhaps he was using Snape's wand, but she pointed out 
that in OoP he is clearly using his own wand in the MoM. From where 
did he get it? I guessed that Lupin got him one or that perhaps Mr 
Olivander is secretly in the Order -- lame, I'll admit; but it's 
late.

I'm sure this has been answered (or discussed) before but amd too 
weary to look it up. Any thoughts, leads, answers?

Thanks,

M.E.