By a few months or so- long enough that Henry VII knows about it but not enough time for Henry VII to remarry and try to sire heirs.
So...
A) Who would Henry VII want to succeed him?
B) Would anyone care who Henry wanted/who would actually succeed?
Of the people with some degree of royal blood...
There's Henry's two daughters- Margaret, who's been in Scotland married to James IV since 1503 and the unmarried 13-ish Mary.
Of the daughters of Edward IV there's...
1) Catherine, whose husband William Courtenay is currently imprisoned (for allegedly plotting with the Yorkist de la Poles). Her father-in-law the Earl of Devon is still around (just- he died a month after Henry IOTL) and her son is 11-13-ish.
2) Anne, married to Thomas Howard (IOTL 3rd Duke of Norfolk). Her father-in-law the Earl of Surrey is still around. However, Anne is 34 and has no living issue.
3) Bridget, a nun.
Elsewhere, there's...
1) Edmund de la Pole, Earl of Suffolk and his brother William, both imprisoned.
2) Their brother Richard, currently floating about the continent.
3) The widowed Margaret Pole (OTL Countess of Salisbury), daughter of the Duke of Clarence, whose eldest son Henry (OTL Baron Montagu) is 14-17.
4) Anne St. Leger (granddaughter of Richard Duke of York by his daughter Anne), married to George Manners (progenitors of the later Earls and Dukes of Rutland).
5) Edward Stafford, Duke of Northumberland. Was ultimately executed IOTL in 1521 for supposedly harbouring royal pretensions. His eldest son is 8-ish, and he has the Earl of Northumberland and the Baron Fitzwalter as brothers-in-law.
Would Henry want one of his daughters to succeed him?
Is there a mad scramble to wed Mary and claim the throne?
Do the Yorkist de la Poles have any chance?
Do we see some weird compromise where either Henry Pole or Henry Courtenay are wed to Princess Mary to form some composite regime?