I've never sent a playlist by private message, but I have sent playlists by email to my main computer to back them up. These directions are for iOS but I suspect they are similar for Android devices:

+ Call up a playlist
+ There is a share icon (a square with an up-pointing arrow) at the bottom of the list. Tap the icon
+ Tap iReal Pro Format
+ Tap Message and go on from there. To send by email, tap Mail and go on from there.

That should do it.