A copy of the First Doctor's mind with all his memories was created during the transference process, when the First Doctor's energy was extracted and stored in two high input vats. When Jano ordered in-transference from these vats, his behaviour was strongly affected by the Doctor's personality, memories and conscience. (TV: The Savages)
After the Doctor left the planet, the copy was placed in a laboratory and supplied with an optical scoop and means of speaking with other inhabitants of the planet. It was connected to the computer systems and tried to help people by answering their questions.
The copy's voice and mannerisms were those of the Doctor, and it had all his memories as of the time of the transference. However, Steven Taylor vigorously opposed calling it "the Doctor" and insisted that "this thing" does not have the same moral standing.
At some point, the copy obtained a permission of Malbenia, a young technician, to try and transfer its consciousness into his body. The experiment failed, and the copy was forced to retreat back into its jar, causing the death of Malbenia. Steven's investigation, however, showed that a successful experiment would have erased Malbenia's personality, replacing it with that of the copy. Despite these findings, Steven did not announce them for fear of retaliation against the copy.
In 1983, when the copy started considering whether to run for the elected office of the king, however, Steven, himself long deposed from the throne and withdrawn from political life, interfered and persuaded his granddaughter, Sida, that the copy's disregard for sentient life disqualifies it from running. After Sida went public with the story of Malbenia's murder, the public outcry forced the copy to dissolve itself into the computer systems before a decision of its termination could be taken. The last words of the copy before its dissolution was a suggestion for Sida to run for the office herself. She successfully followed this advice and became the queen. (AUDIO: The Founding Fathers)
In 1986, Steven, partly possessed by the Vardan woman, managed to bring the First Doctor to the planet from Earth's South Pole, where he was nearing his first regeneration. (TV: The Tenth Planet) The Vardan woman, previously dispersed between Steven and the Doctor, reassembled herself in her wave form. Her goal was to destroy the whole planet as a revenge for the Doctor thwarting a Vardan invasion on Grace Alone, where he had unravelled the Vardans' energy structure with the power of his mind. (AUDIO: The First Wave) Steven, Sida and the Doctor faced the Vardan in the laboratory. Cautious of the Doctor but unaware of a copy of his mind still lurking in the computer systems, the Vardan was lured by Sida's thoughts into checking the computers. There the self-reconstituted Doctor's copy was able to unravel the Vardan much the same way as the Doctor did earlier on Grace Alone.
It is unknown whether the copy merged back with the Doctor during this journey. What can be said for certain is that the Doctor managed to return to Earth in time to undergo a successful regeneration. (TV: The Tenth Planet)