Who allowed Jesus to return from exile and rebuild the temple in Jerusalem?

This did not happen. The Second Temple stood while Jesus was alive and remained standing for four decades after Jesus was killed by the Romans. The Third Temple has not been built.

Jesus was never in exile, didn't return from one, and was never involved in any way in rebuilding the Temple in Jerusalem. Jesus came to earth approximately 536 years after the return of the Jews to rebuild the temple.

An observation:Just in case the question meant to read "Jews" instead of "Jesus" (which would then completely make sense), the answer would be King Cyrus of Persia (Ezra 5:13). Zerrubabel led the Jews, along with Ezra and Nehemiah in the rebuilding of the Temple.