Comparing columns in two different excel sheets and if they match, copy a third column

I need to upload a spreadsheet containing the details of a substantial number of Year 8 pupils, onto a course in the school VLE (Moodle). The fields I will use for the upload are Col A = firstname, Col B = lastname, Col C = username and so on. I have obtained fresh data for Cols A and B from the school MIS, but the MIS it does not contain Moodle usernames, course names etc.

Fortunately, I was able to obtain (ie export) a spreadsheet from Moodle, which contains last year's data (Year 7) for the same group (who are now Y8). It had columns as follows: Col A = firstname, Col B = lastname, Col C = username etc. Pupil's names for my Y8 group are largely the same as last year (when they were in Year 7), although some pupils have been added and some taken away between July 2018 and Sept 2018. Hence Col A and B on S1 and S2 do not match up.

If I call last year's (2017-2018) spreadsheet S1, and this year's (2018-2019) spreadsheet S2. I need a formula which will read Col A and Col B in S2 (the new sheet), and compare the names with the same columns in S1 (last years sheet), and where there is a match (ie names are the same), pull the usernames from S1 and place them in the appropriate row in S2.

This will populate around 85% of S2 with usernames and I can do the rest manually. I cannot simply copy the usernames across from S1 to S2 as the Cols A and B on the two sheets do not match. Please can anyone suggest a way I might do this? The alternative involves a lot of copying and pasting!

Thank you so much for your reply.
I ran the script and named the sheets 'LastYear' and 'ThisYear' as you did.
I keep getting "runtime error 9: Subscript out of range".
Debug highlights the line "Set s1 = Sheets("LastYear")".
I ran the script from worksheet S2.
Would be grateful for your guidance
Thanks again