Can I put an outlet inside of a wall?
No. Section 314.29 of the National Electrical Code (adopted in some form in most localities in the US) requires that all outlet boxes be accessible without removing any part of the building or structure.  That includes wallboard.

You could build a recessed section in the wall that has an easily removed front panel.  You could install an outlet in that section, plug in the charger and then run the charging cable through a hole in that panel.

If the tablet uses a standard USB charger, you can now get outlets that have the charger built in.  Then you just need to plug the low voltage USB cable into the outlet and into the tablet.

 

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