if you wouldn’t want the backup as a possible source for restoring data, then beyond the standard iNat CSV export tool for data (or perhaps in addition to it), you could use this page to get print-friendly views of your observations with options for including most parts of the observation, including photos and maps, which you could then print as hardcopy or to a file format like PDF: https://forum.inaturalist.org/t/tool-for-making-observations-printer-friendly/4513/16. you can read the thread to learn about some of its limitations and to find the source code so that you can adapt it, if so desired.
if your friend can restore his observations using the suggestions i noted above, let me know how he did it, and i can recommend other ways he could back up his stuff in the future. (i want to know how he did it to judge what kinds of tools and scripting languages he is comfortable using.)