You don’t have a Plex Pass. Only a Plex Pass will unlock all mobile apps on a certain Plex account. (and those of its managed users as well)
So that means that you unlocked your mobile app with a one-time payment in your app store.
This one-time payment is not a Plex Pass.
And it is not bound to your plex account. Instead, it is bound to your app store account (the “Apple ID” in this case).
Since your friend uses her own app store account on her mobile device, it doesn’t make a difference whether she uses your plex account or creates her own account.
In order to unlock the mobile Plex app, she’ll have to make the one-time payment as well.