The argument is valid. That's because in logic, we say that an argument is valid if it's impossible for the premises to be true and the conclusion false at the same time. If two statements A and If A then B really are true, then so is B. If both A and If A then B are false (or better, if at least one of them is), then the conclusion might be true or might be false, but the argument is still valid; the conclusion still follows.
You seem to say that if we have no evidence for something, then it's false. But that's not right. Lots of things are true whether anyone knows them. (How many worms were there in the garden plot at noon yesterday? There's only one right answer, but no one happens to know it or even have evidence.) And things can turn out to be false even if we have serious evidence that they're true. And you seem to be saying that if the premises of an argument are false, the conclusion must be false too. But that's not right, and in particular it's not right even for valid arguments. Consider
All dogs are fish.
All fish are mammals.
Therefore all dogs are mammals.
This is a valid argument. No argument with that structure could have true premises and a false conclusion, and that's what validity amounts to. But the premises are false and the conclusion true.
So your friend is right and isn't committing any fallacy. (By the way: fallacy names are over-rated. Most of the professional logicians I know are not good at remembering those names. But they are very skilled at explaining what makes arguments bad.)
Don't let all this throw you off-balance. Anyone who's taught logic will tell you that you're in good company; understanding logical validity takes a little bit of practice and work. But there are very good reasons why logicians define validity as they do, and in any case, the argument form you offer really is a textbook case of a valid argument form. It even has a name: it's called Modus Ponens and it's a basic rule in just about any logic text.