Husky 125 blower vs 125 trimmer engines?

[Forestviller]

I need to do a piston and cylinder on a 125b blower. Oddly the parts must be purchased separately, but the 125L trimmer rebuild is sold as a kit and costs half as much.
I dug high and low through the internet but can't figure out if the two share the same engine, it seems logical that they do but can anyone confirm with certainty?
The individual part #'s are different (of course)...

 

[Conquistador3]

The cylinder assemblies are slightly different on the outside: I am going by memory but the 125B casting is different to allow fitment in the blower body.

 

[Forestviller]

Ah, bummer. Looks like it'll be a part-out.