The starter tent does not allow you to share items with a trusted friend. You need a crafted tent.

All parties you want to access a tent should be friends, and should set each other as trusted friends in the friends management window.

1. Add each other as friends first.
2. Each of you open the Character sheet (C button).
3. Right click lower left or right area of the character sheet, either the body or the hand, Manage, Friends.
4. Set friend(s) as Trusted, Update friends.

Your friend should be able to add and take away from the tent's inventory.