Hi Tom and Norma,
It's hard to know what Phillips took home from Millers Court. If it was body parts then he took them with him to the post-mortem the next day [see below]. Maybe he had an ice-cabinet at his home surgery. I think 1888 was too early for refrigerators.
The Times 12-11-88
"As early as half past 7 on Saturday morning, Dr. Phillips, assisted by Dr. Bond (Westminster), Dr. Gordon Brown (City), Dr. Duke (Spitalfields) and his (Dr. Phillips') assistant, made an exhaustive post-mortem examination of the body at the mortuary adjoining Whitechapel Church. It is known that after Dr. Phillips "fitted" the cut portions of the body into their proper places no portion was missing. At the first examination which was only of a cursory character, it was thought that a portion of the body had gone, but this is not the case. The examination was most minutely made, and lasted upwards of 2 ½ hours after which the mutilated portions were sewn to the body, and therefore the coroner's jury will be spared the unpleasant duty of witnessing the horrible spectacle presented to those who discovered the murder."
It's interesting that in this account Bond was assisting Phillips, and not the other way around. Also that Phillips' "copious notes of the result of the post-mortem examination" have not survived and all we are left with is Bond's report.