FulGaz gives you the option to stop part-way through a ride, save your progress, then pick up again from that GPS location later on. You can do this by using the "Save for Later" option.
When you are part-way through and would like to stop, tap the "<-" button in the top left corner of the screen just under the route profile. You'll be given a few options, but you'll want to choose save for later.
Save and upload your ride as you normally would. This will save your ride data to your Ride History, email you the FIT file and also upload the data to any third-party linked sites such as Strava.
When you go back to that ride again in the future and hit RIDE, you will be given two options.
Selecting START RIDE will start you from the beginning of the route.
Selecting RESUME RIDE will start you from the location on the course where you finished last time. You'll want to choose this resume option.
NOTE: The two rides will still be treated as two separate rides (FulGaz won't "join" the data). You'll be starting your ride from the GPS location on the course where you left off last. The ride will show as two separate rides in your Ride History and two rides on any third-part linked sites such as Strava.
You can do this for all rides except for those in the Training Program collections, which were written and designed to be ridden in one session.