The B3's are made by at least two companies in China, and each is different. Yes, yours has the more simplistic stock, but those seemed to have tuned better for me than those South Summit b3's with the monty carlo stock which seems to have slightly lower abilities, at least with what I do with them.
Can that South Summit stock fit? Yes, but it will need a light reworking, and that is where you're going to have to get it from. They sell their B3 for about $25. It uses a pin to keep the cocking lever in check; the one you have uses the stock itself to rub against. Thus you will need to build up that area of the South Summit stock to keep the cocking lever in check. I used some Teflon furniture slides, cut down and epoxyied in place.
Also don't let those pictures fool you. It is a crap game as to the quality of ANY of those cheap Chinese springers stocks. That is a translucent paint, not a true stain, and can and does hide tons of putty. I found that my Industry brand B3 (the one you have) had nice wood. I ground off the checkering at the base of the stock and added a spare Gamo rubber butt pad. Fits fair enough, and with the walnut stain, I like it. The other one needed a Dupli-Color Truck bed liner paint job to look acceptable after I took off the factory stain (makes it look like a synthetic plastic stock).
Don't let any of this intimidate you. They are pretty darn nice when done. I get low 700fps out of them and can hit within a 2inch circle at 60 yards with a cheap Daisy 3-9+32 Powerline scope.