When you receive a lead from your partner you have two options in Partner Partner for what to do next. You can accept or decline the lead.
You will receive an email when the lead is shared and in Partner Partner will have the the two options on the Leads tab, accept or decline.
Accepting a lead requires clicking the green icon. This will convert the lead to a deal which will then populate your Deals tab. Monitor future changes to deals on that tab.
Declining a lead will keep it in your lead list but with the new "rejected" status.