Your friend is, of course, totally wrong about this--under no circumstances whatever can the English expression 'as well' be written as one word. If he saw otherwise, than the sources he saw were in error. 'As well' written as one word is never correct in English.
As you cannot prove a negative, it is not for you to prove the point. Rather, he is the one claiming that writing it as one word is correct, and therefore, he has the burden of proof of showing that his claim is correct by supporting it with evidence. So, I suggest you turn the argument around, and just say unequivocally, "No, you couldn't be more wrong; if you say it's correct, then show me."
And you might tell him in advance that finding occurrences of 'aswell' on the internet is not enough, as I can quote him 28 million occurrences of the misspelling 'seperate' on the internet (correct is 'separate'). So he must be wary of carelessly using pure search engine counts, as this is not evidence (there are over 9.2 million 'aswell's, and none of them represent a correct usage of 'as well'.)
I don't necessarily always go along with 'official sources' on the internet for trying to prove a point, because they can sometimes be as wrong as your friend is (the many errors of 'Urban Dictionary' is a case in point).
However, if you think your friend is the type to be impressed by such 'official' citations, then maybe you can get him out of your hair by quoting this site: http://www.wsu.edu/~brians/errors/aswell.html
. It's a generally reputable site, and states the case for 'as well' as simply and directly as possible; perhaps your friend will shut up about it now.
Finally, he's welcome to write me directly if he needs an even more forceful debunking of *aswell as one word.