What to do:
-> let Doctor move in
-> make him together with Sarah Wattermach(speak to Rosa Ranek - she knows her)
-> get "Gathering data" quest
-> ask Rosa Ranek about Sarah
-> call to the ministry and tell them that Sarah might be someone else
-> speak with Sarah about original Sarah and tell her you know everything and you will kick her out. Insist about it all along, then she will offer you a coffe in the end of conversation
-> DRINK IT WITH PLEASURE
*poof* achievement unlocked!