After his brain was salvaged, Morbius was transplanted into a new body by Mehendri Solon. An unstable patchwork of parts from various species, topped by a purely artificial brain-case, the "monster" was hounded off the edge of a cliff by the Sisterhood of Karn and destroyed shortly after Morbius had been transplanted in this body. (TV: The Brain of Morbius)
The Imperator as featured or mentioned the Faction Paradox series fills the same place in Time Lord history as Morbius, and the authorial intent is clearly that "the Imperator" be read as a title or alias of Morbius. However, as none of the stories featuring the Imperator held the licence to the character or name of Morbius, this Wiki does not acknowledge them to be the same individual. Interestingly, the Imperator's contemporary in Faction Paradox, the War King, is for his part implied to be a future version of the Master; this would, logically, mean that "Morbius" was a contemporary of the Doctor themselves.
Morbius was referenced in Craig Hinton and Chris McKeon's Time's Champion, a sequel to Hinton's Millennial Rites and The Quantum Archangel. It was revealed Morbius fathered twin children, the Children of Contempt, with an unknown renegade Time Lady.
The Presidents are categorised by in-universe chronological order. Loose chronological order applies for the lists, but when in doubt (as with the temporal uncertainty of the Time Wars), list them in the order in which they were first depicted as Presidents in the real world.