I was an Eramus interchange student in the UK for my final year project 20 years ago.
Whilst I have that in my CV, and even have in the Internet my final report in an old site of mine, I do not have a single proof in writing I was ever there. Even while there, I never had a proper student card, but just a provisory piece of paper.
Come to think of it, the most tangible documents I have ever with me even at the time where the check with the grant money and the programme evaluation form.
My tutor is probably retired. I recently emailed my project supervisor with this doubt, he did not answer.
Note that I myself work in Academia nowadays, and although it is in a different city and unrelated University, I might also pose them this doubt.
The document would come in handy someday, for instance to help me getting the nationality of my wife. What would be the best course of action for getting it after all this time?