For me it doesn't matter how long it is after a sim graduates, and yes by 'move from the neighbourhood screen' I do mean from the sim bin.
I'm afraid I haven't tested lots of different scenarios.
What has happened for me is:
* Sim graduates and is in the sim bin. If I move them to a new house from there, they are fine (just the one graduation memory). If I combine them with another household they are also fine.
* I play them in their house for at least one time and save, but it's often been many sessions.
* I choose move family from the neighbourhood screen and the family moves to the simbin.
* I move them into an unoccupied lot. The sim has a second graduation memory, that appears before the "moved in" memory.
I have now just moved another family with 3 university graduates (2 adults and 1 elder who have been living in their house for several saves). Success - none of them received a new graduation memory.
I hope I've made what I'm doing a bit clearer ! Thanks for looking at this.