Can you tell me the story of how Sai Baba's portrait ended up with Kakasaheb Dixit just before his trip to Shirdi?

Certainly. According to Chapter 51 of the Shri Sai Satcharita, the portrait in question was one that Baba's devotee, Megha, used to worship. The glass on this photograph had broken, so it was sent from Shirdi with Balasaheb to the city of Nagar for repairs. After being fixed, the portrait was kept covered in Mirikar’s drawing room. It was here that Kakasaheb Dixit was staying, eager to go to Shirdi. In a fortunate turn of events, just before Dixit's planned departure with Madhavrao Deshpande, Balasaheb unveiled the portrait and entrusted it to Madhavrao, telling them to go to Shirdi in Baba's company. Dixit was overwhelmed with joy upon seeing the very image of the one whose darshan he longed for.