[discussion thread; thanks to Morines]
Step 1 : Turn off any Internet connection in your cell (mobile data and Wi-Fi), and launch Memrise.[]
When you tap on the course, you should now be able to enter it, instead of getting stuck in the "loading" screen forever (if you get the message "You need an internet connection to view this course", re-connect without closing the app as detailed below, go back to it, and make a new attempt).
Step 2 : Turn on your Wi-Fi connection without closing memrise or exiting the course by tapping on the home key on your phone[]
If you didn't get to download the course yet, you may now want to do so, especially if you have a Wi-Fi connection available.
Go to Settings or Quick Settings, and then turning on Wi-Fi, to finally going back to memrise
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Step 4 : Then click the configuration button and select the available offline option; it may take a while, but it'll eventually set about downloading the levels.[]
Step 5 : After []
As you leave the course, it may take a while for the session progress to be uploaded, or it may even seem frozen.
Pull down the landscape in the main screen while it says "Refreshing...", and release it when it says "Release to refresh...". You must now see how the uploading learning progress bar fills up.