Having performed a number of Custom ROM installations on my Moto G3 2015 (Osprey) smartphone, I think I now have the procedure nailed down. So, for my future reference, and for anyone else who may find these useful, the following are the steps involved in backing up an existing Android system and installing a custom ROM:
1. Download the custom ROM and the associated open-Gapps file (select ARM, 9.0 and pico for Android Pie) and store these files on the phone. I downloaded the files to my PC and then used a USB cable to transfer them to the phone. Note that, when using Windows, it is necessary to ensure that the phone’s USB connection is set to transfer files (sometimes labelled as MTP – Media Transfer Protocol), rather than “charging”, in order that the target folders (i.e. internal storage and the microSD card) on the phone are displayed in Windows File Manager.
2. Install the Official TWRP app from the Play Store. Use this app to download the current version of TWRP (twrp-3.3.1-0-osprey.img at the date of writing this post) and flash this image to Recovery.
3. Now is a good time to make a complete backup of the current operating system – just in case things go south when installing the new custom ROM. Boot the phone into Recovery mode, use the Backup option, and select the System, Data, and Boot partitions to be backed up to the microSD card.
4. Back out to the main TWRP menu and select Wipe – Advanced Wipe. Check the boxes for Dalvik / ART Cache, System, Data, and Cache and wipe all of these areas as a “factory refresh”. (Note – Do not check “Micro SDcard” or this will wipe out any data that you have stored on the supplementary storage medium.
5. Go back to the main menu and select Install. Browse to the folder with the installation files for the custom ROM, select the zip file, and swipe to flash the custom ROM to the phone. Note that the screen may go black as the display times out. But, just wait. When the installation is complete the display will illuminate with the message “Swipe to Unlock”.
6. Select Wipe Cache/Dalvik and wipe these areas.
7. Go back to the Install Zip screen. Select the open-gapps file. Swipe to flash the Gapps utilities to the phone.
8. Select Wipe Cache/Dalvik and wipe these areas.
9. Finally, select Reboot System and your phone will boot into its shiny, new, operating system!