You can convert them via OpenTX Companion. I don't think they will convert on the Radio if it is a different type.
http://www.open-tx.org/
Also the radio can only convert models one major release at a time(2.0->2.1->2.2) but I think the Q-X7 started with 2.2 so that is probably not an issue here.
Remember that different radios have different controls so missing control will be "forgotten" and you will need to re-hookup or re-create an alternative depending on the case.
Also note that for Taranis models like the Q-X7, the SD card does not contain the models unless you made a backup. Hopefully you did!
A full backup is made via the RADIO SETUP VERSION page and writes out the EEPROM content to the SD card in the form of an .otx file. Companion can just load such files and conversion is easy. You just need to change the Radio Type in Settings->Settings... and save the .otx out as a new file.
You can also make individual model backups on the TX, generally to manage the model memory. these save out is a different format that Companion 2.2.X can't load directly...(not sure why, think its a bug) If you have these then you can use the OpenTX Companion Simulator and a copy of the SD card to load them and write out a backup file.
The Horus works differently in that only the current model is in memory and the rest are stored on the SD card.