'Proving' it is always relative of course, but I think we've got plenty of things that are enough to not make anyone doubt: several years of Facebook posts (yes, that counts), plenty of evidence of having gone to places and events together (like tickets and photos of tennis and volleyball tournaments), flight tickets, many, many photos in the Netherlands, Brazil and several countries where she's had competitions, even official results of the half marathon we ran together last year (including photos) where we finished in the same second. If that's not enough yet, they can easily look at online forums (like here) where it has been pretty clear for quite a while. Besides, plenty of people can provide backup if needed, ranging from (former) colleagues of mine to international biathletes (including from the World Cup), who are friends of her and have also met me (introduced as her boyfriend), and so on.
They're really not going to spend a lot of time investigating a story where everything checks out (because it is actually true), just for the 0,001% chance of catching a fraud, whereas other people who - unlike us - really do try to fool them are often way easier to catch.