Yes, make a digital copy of NOA2 and keep it.
I'd say keep all original I-797 letters for all cases including future cases (I-129F, I-485, I-751, N-400).
Make digital copies of them too and store in the cloud.
In the end, your fiance will have about 20-40 pages of important papers from USCIS documenting their immigration journey. Government may always ask to re-prove / re-verify how they became a citizen, even many years later. Either for them or descendants. Along with house deed and their birth certificate, these are super valuable docs.