He remained relatively unknown in his time, not being inclined to push himself forward, and suffering, according to David C. Douglas, from a "persistent lack of bare recognition".
In 1647 he was elected to a scholarship at Corpus Christi College, Oxford and placed with Zachary Bogan as his tutor.
Along with another scholar of Corpus, one Timothy Parker, Fulman had deliberately 'blotted' and 'torn out' the name of Edmund Stanton, the parliament's choice of college President, which the visitors, on 11 July, had entered in the buttery book in place of Robert Newlin, who had been expelled as President.
When twenty-one years old he became, by Hammond's introduction, tutor to the heir of the Peto family of Chesterton, Warwickshire, in which capacity he continued until the Restoration.
[2] Fulman was the author of: He collected for publication the so-called Works of Charles I, to which he intended prefixing a life of the king, but, being taken ill with smallpox, the bookseller, Richard Royston, engaged Richard Perrinchief for the task.
He also collected materials for the life of John Hales of Eton and for that of Richard Foxe, bishop of Winchester, with an account of the distinguished members of Corpus Christi College.