The determining factor is the carburetor, not the version of M-tronic, though the white solenoids are generally associated with v3 systems. It's my understanding that there are fitment issues between the different carburetors with how the white solenoids actually seat. Older solenoids will still work just fine on the newer carbs, but not the other way around. That may be why Stihl finally lowered the price of the white 5104 solenoids from $85 down to $35.50 like the 5110 always was (and the re-introduced green 5111 now also is). Guys were just replacing plugged 5104s with 5110s for half the cost.
But as mentioned, that saw should use a black or green solenoid unless the carburetor has been changed to one that accepts the white one. Your dealer should know that.
And while I've seen reference to v3.0 MS261s in print, I've still yet to see or hear of anyone actually having one domestically. Anyone?