Yes, you can copy it anywhere you like - to another style, to another variation in the same style, to another variation in the same style ....
....but make sure the style parameters are set up the same for the two variations you are moving between i.e. bar length, etc. The bar length is nearly always different between style variations in the same style. So you need to make them the same first, and that might not work too well with other parts.
Mike