The starter tent does not allow you to share items with a trusted friend.
All parties you want to access a tent should be friends, and should set each other as trusted friends in the friends management window.
Your friend should be able to add and take away from the tent's inventory.
A GM may opt to create replacement tents for a group that wants to share tents. Create “tent”, which is a replica of the starter tent, but doesn't have the restriction.