Look at this excerpt from a <PERSON> article by <PERSON> (the full article can be found here):
The wizarding family of <PERSON> descends from the twelfth-century wizard <PERSON> of Stinchcombe, a locally well-beloved and eccentric man, whose nickname, ‘the <PERSON>’, became corrupted in time to ‘<PERSON>’.
<PERSON>’s eldest son, <PERSON>, married a beautiful young witch by the name of <PERSON>, who came from the village of Godric’s Hollow. She was the granddaughter of <PERSON>. In the absence of male heirs, she, the eldest of her generation, had inherited her grandfather’s invisibility cloak. It was, <PERSON> explained to <PERSON>, a tradition in her family that the possession of this cloak remained a secret, and her new husband respected her wishes. From this time on, the cloak was handed down to the eldest in each new generation.
The <PERSON> continued to marry their neighbours, occasionally <PERSON>, and to live in the West of England, for several generations, each one adding to the family coffers by their hard work and, it must be said, by the quiet brand of ingenuity that had characterised their forebear, <PERSON>.
<PERSON> ... , who was a direct descendant of <PERSON> and <PERSON>, ... 351
served on the Wizengamot from 1913-1921.
<PERSON>’s son was called <PERSON>. ... It was <PERSON> who took the family gold and quadrupled it, by creating magical Sleekeazy’s Hair Potion (‘two drops tames even the most bothersome barnet’). He sold the company at a vast profit when he retired, but no amount of riches could compensate him or his wife <PERSON> for their childlessness. They had quite given up hope of a son or daughter when, to their shock and surprise, <PERSON> found that she was pregnant and their beloved boy, <PERSON>, was born.
<PERSON> and <PERSON> lived long enough to see <PERSON> marry a Muggle-born girl called <PERSON>, but not to meet their grandson, <PERSON>. Dragon pox carried them off within days of each other, due to their advanced age, and <PERSON> then inherited <PERSON> Invisibility Cloak.
From the above, it is quite clear how the Cloak came into <PERSON>' possesion. 725