Normally you’re not supposed to place new files into the main texmf tree under /usr/share/texmf. User installed files are supposed to go into your own private texmf tree.
If you look into /etc/texmf/texmf.d/05TeXMF.cnf you’ll see that it defines a folder in your home as your private tree:
So, the official solution is to create this directory in your home and place the put into it. I’m not sure if you need to recreate the tree structure, but it won’t hurt to do so. I guess class files would go into ~/texmf/latex/base/AGUtex.cls
% This used to be HOMETEXMF.
TEXMFHOME = $HOME/texmf
Afterwards I suppose you have to run mktexlsr on it.
Then, to make sure it is found by the TeX system you can check