The PSR-E and PSR-I models don't have a Style Assembly feature for saving and exporting styles, as can be done on the PSR-S models. The only way I know of that you can even attempt this is to record a style in a User Song, save it to SMF, and then use third-party software to try to create a style file from the SMF. I say "try" because even though it's possible to create a style file from a MIDI file, you would need to recreate the original CASM section, which might be extremely difficult to do, given that you would have no way to know how complicated the original style is as far as things like using alternate source channels for specific keys and chord types, plus the Indian styles might use more than just destination channels 9 and 10 for kit voices-- which raises another issue, the voices and kits used.
And as far as trying to use another keyboard (PSR-S or Tyros) to control the style playback on a PSR-I, the PSR-E and PSR-I models do not have MIDI settings that let you assign an incoming MIDI channel for controlling chord changes in their onboard styles, as can be done on the PSR-S models. You can send Start and Stop messages if the PSR-I is set to External Clock, in which case I think you can also control the Tempo by the external MIDI clock pulses, but there is no way to control the style section changes and chord changes externally.
Aside from playing the PSR-I and the PSR-S or Tyros at the same time (the best solution, IMHO), one possibility if you don't want to have to keep different hands on different keyboards might be to record the desired PSR-I style to a User Song, complete with all of the desired section changes and chord changes, then set the PSR-I to External Clock, select the desired User Song, and try to send Start and Stop messages from the PSR-S or Tyros to activate the User Song while you're playing the PSR-S or Tyros. But that might be tricky.
