There is no specific property for the originating stencil, but you may be
best advised to listen to the MasterAdded event
During that event, the Master object will be given a unique name for the
document you are dropping into, but the BaseID will be same as the Master in
the originating stencil. Therefore, you can iterate through the open
stencils to get the Master with that BaseID.
As soon as the MasterAdded event is over, the new Master will have a new
BaseID, so it will be too late to get the originating stencil, so consider
updating the local Master, or SolutionXML, with the the originating stencil
name, or whatever you want.