I don't think you've done quite enough troubleshooting yet.
Assumptions:
a. A fully charged good battery installed.
b. Battery terminals and cables clean and well connected to both the engine case and the solenoid.
1. Very the above assumptions are correct.
info: The starter motor uses about 150 amps to spin the engine. Note that this amount of power heats things pretty quickly.
2. Test motor by bridging the two large posts on the solenoid. I use an old pair of pliers I don't care much about. Arcs and sparks happen if the starter motor spins. If the motor is shorted, the pliers might become welded to the posts. Knock it loose as fast as you can if that occurs.
Outcome: Motor spins - motor okay. Motor doesn't spin - remove motor and inspect cable from solenoid to motor. If cable good, replace motor. If cable bad, fix and repeat above test.
If motor now spinning by bridging solenoid.
3. test solenoid.
Jumper battery 12 v and battery ground to the two small posts.
Motor spins - Solenoid good.
Motor doesn't spin - solenoid bad.
If solenoid clicks but doesn't engage starter motor, you can try to take solendoid apart and recondition main contacts. If it won't even click then replace solenoid.
4. If solenoid checks good, then bike wiring is faulty. Clutch disengaged or neutral switch provides ground to one solenoid post. And, the starter button provides 12V to the other post Y/R. Find out what is missing and fix it.
Cheers,
P.S. I don't know if a 750 starter motor will fit in the 550. The shop manuals use the same specs for the two. But, no dimensions are given.