that functionality is called referral now, as in tracker web.
Your user will require to have the org unit as capture OU.
To refer an event or a TEI you have t be in the TEI dashbaord, then press the “+” button in the bottom right corner and chose referral (you will see Referral, Add new, Schedule new).
In the next step it will ask you if it is one time (only the event) or permanent (move the TEI)