All I'm talking about swapping are small engine magneto coils with square center holes configured to fit around square sections of lamination packs.
Some lamination packs are "E" shaped, and they fit the coil onto the center, open ended portion, as commonly seen on Tecumseh engines.
Some lamination packs are "U" shaped, and they fit the coil onto the
closed-ended section of their form.
While "E" lamination-fitted coils are easily removed by sliding them off their press fit, "U" lamination-fitted coils can also be removed, though with more effort as the lamination packs must be disassembled, the reverse of how they were assembled and pinned together when the factory built them.
I see NO reason all these magneto coils can't be interchanged unless the square hole size is different or the space under the flywheel is too small to provide clearance. So swapping a Briggs & Stratton magneto coil onto a Tecumseh engine may be possible. Functionally, those coils perform identically. If they don't physically fit, that's another issue.
I did NOT mention nor intend to switch this to a CDI ignition system. So I'm not sure why you mentioned that.
Just for the fun of doing something that may not have been done before, I may install a B&S mag coil on this HS50 Tecumseh. If I do, I'll report back to you about the results from that effort.