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Hello and welcome! My name is ***** ***** I will try my level best to help with your situation or get you to someone who can.
do I have any rights to shed
Not at this point, but if you follow the proper procedure, you could end up with it..
What the person has done by leaving their property there is create a "voluntary bailment" with you being the bailee. A voluntary bailment is when one party, the bailor, leaves personal property in the possession of the bailee with permission or consent. The bailor can return and take possession of the property at any time before the bailee terminates the bailment and the property is considered abandoned. A bailee can terminate a voluntary bailment by giving notice to the bailor that they need to come get the property or it will be considered abandoned and disposed of.
In order to legally terminate the bailment, you have to give written notice to the bailor at their last known address (which would probably be the property address or girlfriend's address if you know it). I would send it certified mail as well as first class mail in case they have a forwarding address with the post office. State that you are terminating the bailment and the bailor has 7 days to remove the property or you will consider it abandoned and dispose of it. On day 8 if it is still there, you can do whatever you want with it and can consider it as abandoned.