Remote storage tablet

 A me and a few friends had the idea of making a mod that had a remote storage tablet. It would basically connect to a storage center and would take the items from there.

 I've sorted out the whole "connecting to the storage center" part. What i need help with is actually getting the items from the inventory. My idea was opening a GUI at the block's position (saved in NBT tags), but it doesn't work. There doesn't seem to be an "open block inventory" procedure block either.

 Does anyone have a solution to this? Thanks in advance!