You should be able to install the update yourself with Samsung 's Smart Switch maintenance utility. If you have a carrier-branded device, they may have included their own maintenance and update utility. Both tools will grab and install the update you need. It will be the same update that you would have received with an OTA update.
Before you do that though, try clearing the app and system caches (app cache first, then system cache). Your wife's phone may have started the download and been interrupted. If there is a trace of the downloaded update package on the device, that could prevent the phone from grabbing the update on its own.