Here's some quick information that I was able to look up:
Activated carbon filters will remove chlorine.
Activated carbon filters will NOT remove chloramine unless the water spends Several minutes flowing through the carbon (ie. Not a filter that just spits water out)
filters will NOT remove chloramine.
So - I'd say the best thing to do is try and figure out what the exact model number of you fridge is, and then do an online search and you may be able to find a digital copy of the manual. Because if you use this thing for fish, you should not only know what it filters, but also if it needs replacements on a regular basis and to make sure your landlord has that covered.