Hello out there!
As fas as I know, there are two different types of starter motors. That one mostly is used is the kind with the pole on the cylindric part. The other one has the pole for the cable on the mounting brace.
Each one designed for the LS650/S40 will fit and work.
Sometimes it happens, that the carbon brushes inside are worn out. That's bad, because they will make costs like a good used starter motor and a bad work fiddling them out and in, including soldering work with a strong soldering iron.
Sometimes it happens, too, that the dust of the carbon brushes together with the grease inside the motor will block the brushes into their guides. So they cannot be pressed correctly against the commutator by their springs. Just take the starter off, do some markings on the end caps and the cylindric parts, take off that two long bolts ans carefully take off that end cap with the two mounting holes. Take a bottle of brake cleaner, rinse well, let it dry well and try again.
If the carbon brushes are really worn out, have a look for another starter engine. They should be about 70-90€ in europe, excl. shipping.
And do a little prayer it's a good one. Replacing the brushes is very fiddly with good chances to break some plastic insulators.
You may choose your way
But first, tell us how you found out the starter itself has gone.
A bad Battery or bad contacts on her and on the ground cable to the engine may confuse you as well!
Regards,
Lou (Germany)