Q: iPhone 5S won't update

We have a two iPhone 5s plus an iPad. Yesterday one iPhone and iPad were updated.Today tried to update wife's iPhone 5S. Install now selected, have to sign in again, then then reports, during "verifing update",  "not connected to internet". WRONG! Can browse via Safari, can got about anyplace, but update software says not so just going into loop. Turn off and then back on. Reports connected. Disconnect and reconnected. Work to browse but not to update. Current runing 9.2.1 on her phone