By default, tracklog recording is enabled only when the device is on and the Memory-Map app is displayed on the screen. Memory-Map also has the ability to record a tracklog in the background, i.e. while the device is turned off, or while you are using another app.
Tap Menu, Settings, GPS Settings, and enable "Record Track While App is Backgrounded".
Use the "Home" button if you want to switch to another app. Don't use the "Back" button as this will shut down the app and stop the track recording. You can also just use the power button to turn off the screen.
While Memory-Map is running in the background, it must be able to display a small notification icon 
at the top left of the screen. If you disable this notification, then Memory-Map won't run in the background and won't record your track. In the Android Settings app, look for something that controls the notifications for each app (device-specific). It may be under Apps, or it may be under Notifications. All the notifications for Memory-Map should be enabled. There may be a setting called "Memory-Map Service" which needs to be on.
Under the Location Settings (App info, Permissions, Location... or other device-dependent place in the settings app), go to the settings for the Memory-Map app. There should be an option to enable the location service to "Allow while using the app". Don't worry if it doesn't offer "Allow all the time". As long as the notification icon described above is displayed at the top left of the screen, Memory-Map is considered to be in use (technically, it is running a "foreground service"). The "Allow all the time" option permits an app to use the GPS without giving any indication to the user that it is running, and many devices do not permit this kind of service.
Furthermore, many devices have an operating system feature to prevent apps from using too much battery power when running in the background. We recommend disabling any device power management features, or setting up Memory-Map as an exception, so the app is not killed by the operating system. If you are able to see the notification icon when you start recording the track, but it later disappears for no apparent reason, it is because the device has killed the app to save battery or to protect your privacy. In the settings app, under Battery, or Power, look for things like "Battery Saver", "Adaptive Battery", "Stamina mode" etc.,
If you find something called "App Power Manager" in the settings, you have to add Memory-Map to the list of "Unmonitored apps". This is a feature of Samsung Phones that is designed to stop processes that use power.
In summary, to record a continuous track while the phone is off or running another app:
- Use Menu > Settings > GPS Settings > Record track while the app is backgrounded
- Tap "Start Logging" on the data panel (the button changes to Stop Logging while it is recording)
- Press the Home button and ensure the Memory-Map "Recording Tracklog" notification is present (top left). If it is not shown, ensure the "Memory-Map Service" notification is enabled in the Android Settings.
- Disable any Power-saving schemes in the device Power settings (this is device dependent)
- In the system App settings, select Memory-Map and ensure the Location Permission is enabled, "While Using the App" is fine.
- Don't use the "Back" button to leave the app. Use the "Home" button.
- Finally, remember to tap "Stop Logging" when you finish your track, because using the GPS does use a lot of battery power.