I’d say def no to sharing, for me my music library is what makes me unique as a DJ,
Also whats exciting about doing a back to back with another DJ is you don’t know what they are going to bring to the table – if its your collection you loose that wild card factor of b2b playing.
Lastly its so easy to DL so much material for free, theres no excuse for your friend to use another DJ’s library.. I’d just tell him he better get busy on Soundcloud and bandcamp so much available for free.. thats after all what a DJ does compile their own database of sound.
Lastly there are all the ethics about sharing music even if you have paid for it or it has been sent to you personally, I’d argue thats its not really yours to share with other djs anyway.