Hi @BarryHattle ,
Could you please share a bit more about the Data card in your screen3? Is it a ComboBox or a TextInput box?
Do you add a Gallery control in your Screen3 to display the searched result?
Based on the needs that you mentioned, I think a collection variable could achieve your needs. I assume that the data card that you mentioned in your Screen3 is Text Input box, is it true?
You could consider unlock the corresponding data card in your Screen3, then add a "Search" icon into this data card as below:

Set the OnSelect property of the "Search" Icon to following:
ClearCollect(
UserProfileCollection,
Filter(Office365Users.SearchUser({top: 999}), DataCardValue.Text in DisplayName)
);
Set(ShowUp, true)
Set the Items property of the Gallery to following:
UserProfileCollection
set the OnSelect property of the Gallery to following:
Set(CurrentSelectedUser, ThisItem.DisplayName); // Store the selected user name from your Gallery into a variale
Set(ShowUp, false)
Set the Visible property of the Gallery to following:
ShowUp
Set the OnVisible property of the current screen to following:
Set(CurrentSelectedUser, Blank())
Set the Default property of the Text Input box within the Data card you mentioned to following:
If(!IsBlank(CurrentSelectedUser), CurrentSelectedUser)
Please consider take a try with above solution, then check if the issue is solved.
Best regards,