When I check for updates, my phone says:
We are currently unable to check for updates.(80072efe).
How can I fix this?
That error code normally indicates
ERROR_INTERNET_CONNECTION_ABORTED i.e. The connection with the server has been terminated. This might be due to a poor network/WiFi reception, either locally, or between you and the servers.
It may be worth trying again later, when there's a better connection; and if this doesn't work, it might be worth backing everything up and trying a hard reset of the phone.