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There ia a way to do this, i dont like it, and will never use it, but for a short time with users i now , it may be ok. The problem is that thay can edit email address too.
If you still want to do it this way.
Go into Admin "Control Panel"
Then go to "System Options" --> "Groups"
select Modefy on "Registered Users"
Find "Module Admin rights" and set the select box "User Profile"
"Learn from the mistakes of others; you can't live long enough to make them all yourself."