One of my players bought a premium module for our group hoping we could use it for our games. The module in question is the Harrow Deck from paizo but I’m unable to upload it to my game, it simply gives me an error about an invalid signature. Is it not possible to share modules within a group?
Heya 
The module is a Foundry Premium module, so you can only use it if you have activated it on the Foundry account that your Foundry key is linked to.
This should help you out Installing/updating Licensed Premium modules
I see that is somewhat of a shame. I suppose a followup question I have is if I’m trying to install a premium module I am subscribed to through patreon, like for example the animation module by Jules and Ben, would that take up space in my asset library or is that essentially taken care of by forge and don’t take up space for me personally?
The JB2A Patreon pack is available on the Bazaar and is not a Foundry Premium pack, yeah 
If you link The Forge to your Patreon account here and install that from the Bazaar, then it won’t take up your asset space but will instead point to the Forge-hosted Bazaar version.
Coolio! That is at least good to hear, thank you for the assistance.