Thank you for posting this on G2G!
It would be worth reading this page about Reliable Sources for pre-1700 profiles in England. For example, we don't consider user-contributed family trees on websites such as Ancestry or MyHeritage to be reliable sources for these older profiles. The most reliable sources are those that were created at the time the person lived, such as parish registers of baptisms/marriages/burials, wills etc.
My first question about Henry Hodgkinson’s profile is whether he is one of the two Henry Hodgkinsons who were aldermen of Preston, Lancashire. If it is, then there is a pedigree for him in the Visitation of the County Palatine of Lancaster in 1664-5, pages 142-3.
The elder of the two aldermen was the “Henricum Hogekynson” who was an alderman in 1542: see The Rolls of Burgesses of the Guilds Merchant of the Borough of Preston Co. Lancaster. 1397-1682, page 15. His father William was living in 1500/1 (16 Henry 7). I would say he was an earlier generation - and that he lived too early to have died in about 1621 and to be the father of Molyneux Hodgkinson (baptised 1663) who is attached as his son.
The younger of the two aldermen Henry Hodgkinsons seems to be a better fit for this profile. He died in 1615. He was the son of a William Hodgkinson and is known to have had four sons: William, Roger, Richard and Thomas.
Ian, co-Leader, England Project