If you firstly ensure your new user has edit own page access to the same custom area.
You can then use data transfer in the admin tab to transfer data from one user to another.
Once in data transfer select the area from your area explorer.
Select your current user from the source box list and then select your new user from the target box list then click get data.
Please note: This will overwrite all current data that exists on your new users page.
If you have any questions, please do not hesitate to contact us via chat.