Q. on H1B FY 2005

Currently, I want to apply H1B FY2005 which requires US Master/PhD. I am a H1B hold in a university and also a part-time PhD studnet. Currently, I have passed the final defense(end of May), and satisfy all the degree requirements. However, the offical diploma will only to me in the late August.
Right now, I want to transfer to a company, can I apply the H1B for US degree holder) with one letter from the Univ.? Which content should be included in the completion letter? Thanks