The exact relationship between Henry and John Cort seems to be unknown
but Henry Cort did come from Lancaster and there was some kind of family connection..
I cannot find any reference suggesting that Henry Cort himself was involved in either trading products produced by enslaved people or owning them although members of the Cort family certainly were, as noted in Jenny Bulstrode’s paper.
Amongst other references see van Batenburg, A. J. V. I. Kort historisch verhaal van den eersten aanleg, lotgevallen en voortgang der particuliere Colonie Berbice. Amsterdam: C. Sepp Jansz, 1807.
(The “kort” in the title is the Dutch word for “short”. The names of members of the Cort family can be found in the document)
However, this has no bearing on whether Henry Cort learnt about Jamaican iron working from John Cort.

The relevant documents at the Devon Heritage Centre are not available online so I have relied on :
Goucher, C. L. 1990. John Reeder’s foundry: a study of eighteenth-century African-Caribbean technology. Jamaica Journal 23,1:39–43.
This is available starting at
https://ufdc.ufl.edu/UF00090030/00064/images/40
“The Reeder Foundry
The descriptions of technical machines and equipment were vague (except for the mention of the reverberatory furnace). It can be noted, however, that multiple furnaces were in use and the operations (given the range of products) were broadly multifunctional: casting, turning, forging, refining and possibly smelting.
According to the records, the eight acres of land purchased by Reeder contained ‘houses’ (more than one) and other buildings.6 Foundry workers included two hundred and seventy-six ‘Negroes’ and between thirty and sixty Europeans; the latter were employed on an occasional basis. The European presence was short-lived for several reasons. Skilled workers were difficult to lure to the Caribbean and expensive to employ, even on a temporary basis (as for setting up operations or training labour). Another reason is found in Church of England records which confirm a high mortality rate among the small population of English craftsmen.”

“The testimony brought to bear to support John Reeder’s attempts to obtain compensation for the foundry’s dismantling clearly indicates that the foundry was ‘of great use’ to Jamaican society in the eighteenth century. Various descriptions confirm the foundry’s working of both iron and non-ferrous metals, including brass, copper, and lead. A variety of articles was manufactured: large iron boilers, iron rollers for pressing canes, cast utensils, a brass train of artillery, brass howitzers, mortars, petards, cannon, shot, lead bullets, plus the general outfitting of British warships and other vessels. Admiral Sir Joshua Rowley testified that without the foundry no fewer than seven ships ‘otherwise would have remained in harbour until supplied from Europe’.
According to one of Reeder’s own descriptions, the foundry equipment had included ‘machinery for making bar-iron’.4 One solitary reference [letter from John Reeder to George Rose, 5 April 1787, Reeder Papers] makes mention of the foundry’s ‘reverberating furnaces’ having been demolished.
The article also says ”
At least one other died as a result of the trans Atlantic voyage, having been brought to Jamaica at considerable expense in about 1783 to restore the foundry. Thus, John Reeder was forced to rely on the skills of African and African-Jamaican metallurgists.
By Reeder’s own estimate, many Africans were ‘perfect in every branch of the iron manufacture so far as it relates to casting and turning… and in wrought iron…’
The Church of England records confirm that both slaves and free Maroons were employed in the foundry. Maroon smiths were highly valued.
A 1743 observer noted:
“The rebellious negroes in St. James forge their own ironwork, making knives, cutlasses, heads of lances, bracelets, rings, and a variety of other kind of necessaries, they have bellows which are made of wood… having for that purpose two negroes who… are always working them up and down.7”
4. Jamaica House of Assembly Journal, vol 8, 7 December 1785, p. 132;
Reeder complained that the machinery had been rendered totally useless and would remain so until people with the proper skills to put it in order were brought from England. One craftsman who had been so engaged at an expense of £140 died too soon after his arrival to have accomplished anything, according to Reeder.

The Black metallurgists were highly skilled.
It is a pity that the material about Henry Cort was introduced into the paper as the conclusion states that this was not intended to be the central concern of the paper.
“Euro American accounts have often described the combination of processes for which Cort took credit as one of the most important innovations in the making of the modern world. But the theft of this combination from Black metallurgists in Jamaica who
developed it was not the central concern of this paper.”.

I would prefer Jenny Bulstrode to revise the paper by removing the sections which reference members of the Cort Family. The paper would also need a new title.
This revised paper would still satisfy what is stated to be its main purpose.