If it worked on the stand with the old stator then the problem isn’t with the stator. We’re so quick to replace everything nowadays!
If if I had to guess, no spark means the green (ignition) wire in the loom is shorting to ground. A simple check is to hold the green from the stator to the frame and see if you get a spark jump. It should because you said it was running.
A 125 special should have a key ignition switch. Make sure it’s in the ON, one or more click to the right of center position (sounds obvious I know but you wouldn’t be the first)
If that doesn’t work then separate the loom out of the problem. Process of elimination. Only connect the green wire from the stator to the coil and coil to ground. This way it’s basically like you had it on the stand. From there start putting it back together. At some point it will stop running and there’s your problem.