What should I do with things my friend left with me and forgot then traveled, and I cannot reach her; should I give their value as zakat on her behalf?

You must keep your friend's belongings and look for a way to contact her and send them to her. If there is no hope of her returning, then you may give them away in charity on her behalf and write this in your will. If she returns, she has the choice to approve the charity, or take items similar to her needs, or their value. And you will have the reward for the charity.