And per the Lucky Cheng's Twitter feed:
A look back at our humble beginning. Mr. Cheng with the original 1993 staff: Tora, Poupée, Mama Mei-Ling, and Daisy.
Not sure when they are actually moving up to Times Square. There have been a lot of different dates mentioned via various sources. So we'll just go with "soon."
Meanwhile, for more on the Lucky Cheng's building on First Avenue at East Second Street, Jeremiah's Vanishing New York has a nice history of the space here.