Should I send my transcript to the university I'm going to be?
It is quite normal for applications (including transcripts) to be submitted and processed, and indeed for offers of admission to be extended and accepted, before the last semester is over. Very rarely will an offer of admission be contingent on academic performance in the last semester. However, all offers of admission to graduate programs are contingent on successful completion of the program (meaning, you cant flunk out in your last semester and fail to graduate). So, you will have to submit a final transcript to the university which accepted you when you have graduated. It is not going to be automatically updated.