Green’s Dictionary of Slang

to offer credit, to defer payment, to record as a debt.

1725		New Canting Dict. n.p.: Hang it up [...] Speaking of the Reckoning at a Bowsing-ken, when the Rogues are obliged, for want of Money, to run on Tick.
1785, 1788, 1796		Grose Classical Dict. of the Vulgar Tongue.
1811		Lex. Balatronicum.
1823		Egan Grose’s Classical Dict. of the Vulgar Tongue.
1846		Swell’s Night Guide 121/2: Hang it Up, to leave a reckoning unpaid at a public house.
1859		Matsell Vocabulum.
1880		Nat. Police Gaz. (NY) 9 Oct. 6/4: ‘Your reverence, I’m sorry for to be obliged to hang this little bill up’.
1895		Crowe Aus. Sl. Dict. 35: Hang it Up, remember it.