To add to Aaron's answer:

As a distant cousin of (Hugh) McCulloch mentioned in Aaron's answer may I just correct the impression that he "split". He was writing letters with instructions to Hartnell from different missions in California until at least 14 August 1823 and on 1 March 1824 he writes from Mazatlan which he was temporarily visiting being by then based in Callao:

https://archive.org/details/documentos3305189994vall/page/n34/mode/2up

(my transcription)

"I take the whole of the management of the Californian business into my own hands, having only to consult with him [John Begg] as to the disposal of the produce, chartering vessels etc. so that if you play your cards in that quarter, as well as we will ours in Peru, and our friend in England, I have no doubt we will make a very handsome thing of it, although what has come to the
Lima market as yet has been a losing concern.”

To quote from Dakin:
"In the spring of 1824, McCulloch left the California scene for good. It was decided that the firm would benefit by one partner remaining on the coast, while the other returned to live in Lima, to supervise the selection and disposal of cargoes in South America and, only occasionally, to act as supercargo on coastal or European voyages. Hartnell was the logical choice to manage the company affairs in California, if he could conquer his old weakness".

After the business of McCulloch & Hartnell was wound up Hartnell failed to pay his share of the losses and on 2 June 1831 McCulloch wrote to Hartnell:

https://archive.org/details/documentos20710002vall/page/n41/mode/2up

(my transcription)

"I have paid Mr Begg my full proportion of all losses and hope that some day or other you will be able to reimburse me if not for all at least part of said Acct"

Also, according to Dakin, referring to Dr. Stephen Anderson, who was acting as go-between between Begg and McCulloch in Lima and Hartnell in California:
"On April 15, 1833, his onetime partners gave Hartnell a full discharge of all debts. Anderson wrote this welcome news to California, with the added assurance that throughout the whole transaction McCulloch had proved himself a good friend."

I realise this answer does not relate directly to the question but I do wish to make it clear that from all accounts and by this and other actions Hugh McCulloch(1793-1842) was an honourable man.