Filtering A LONG List To Entries In A Shorter List

I have a list of email aliases for my company, approx 10,000 entries, mapping the alias to an email address. Two columns, one the alias firstname.surname, second column being the full email address. I have a second list, a subset of these aliases, approx 1200 of them, that are users of a particular web app. All i have in this list though, is the firstname.surname bit.

What I need to do is compare the lists, and where the aliases match I need to pull out the corresponding full email address from the long list, so I have 1200 aliases in the shorter list, with the full email address mapped to it. Is this possible in excel? i've tried all sorts of LOOKUP functions, and MATCH functions, but none seem to work. MATCH will give me the corresponding row number in the long list, but then it seems to offset itself every row it goes down, so the values are 1 out for every row. First row is good, second row -1, third row -3, fourth row -4 etc.

I don't want to have to manually go through 1200 entries and match them against a 10,000-entry list. Hopefully there's a quick way in excel to filter the long list down to the entries specified in the short list?