He was "heir-presumptive" because his position was potentially temporary if Richard had born a son. Who was Edmund? Why was he considered appropriate as a potential king of England? What happened to him after 1399?
Edmund's father was Roger Mortimer, the 4th Earl of March. Roger's mother was Philippa, 5th Countess of Ulster, the daughter of Lionel of Antwerp, son of Edward III (and first "boss" of the page Geoffrey Chaucer). Edmund's parents and grandparents on both sides raced back to kings of England. Edmund's father had been made heir-presumptive, but his death in the Ireland campaign in 1398 caused the position to fall to Edmund.
Richard II was deposed by Henry Bolingbroke on 30 September 1399. Edmund was seven years old, and clearly not seen as a threat to Henry, even though his lineage gave him status as heir to the throne above the right of Henry.
Henry had no quarrel with the young and fatherless Edmund. His mother, Eleanor of Holland, had already remarried. Henry placed the child Edmund into the care of a Sir Hugh Watertown, a trusted servant and attorney of Henry's father who now served Henry. Edmund was raised with Henry's own children, the ten-year-old John and five-year-old Philippa.
"Keep your enemies closer." Henry might have intended to raise Edmund as a loyal member of his household and court, ensuring that Edmund never saw Henry as a usurper. There were those—relatives of the young Edmund—who knew how to reed a geneaology table and knew that there was a chance to replace Henry with Edmund and bring control of England back to their side of the family.
It only took a few years for an incident in Wales to turn into an opportunity for rebellion. This rebellion—entirely unconnected to anything Edmund would or could do—affected events and made Edmund less safe. I'll explain tomorrow.