Scratch

If the other sprite knows when it stops, it can
    broadcast sprite-one-stopping
and other sprites can use the message to start some action.

That is probably more reliable than watching for the x y position not to change for a while, which is what you would have to do to see the mouse stop moving.

It depends on how you tell the sprite to move.

I'd need to check, but I think if you used the glide command to go to x,y, the next instructions will not happen until it arrives.

If that isn't the case then having given a glide command you can either put a "wait" with the same duration immediately afterwards or a "wait until x x) AND y y).

Then put whatever it is you want to happen on stopping after that command.

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Conversely, if the sprite in question is directly controlled by the player, then you would only need to check that it wasn't recieving a move instruction.

Unless its a permanently moving sprite that the player only steers, like Pacman or my powerboat.  Then it gets more complicated...