Green’s Dictionary of Slang

prop v.2

[abbr. SE propose/proposition]

to suggest or propose; to proposition sexually.

[UK]‘Charles Raven’ Und. Nights 16: It had been propped to Bunge by Monty Rose.
[US] in T.I. Rubin Sweet Daddy 11: I’ve been proped [...] you know, propositioned, proposed, see?
[US]B. Rodgers Queens’ Vernacular 84: to make a proposition [...] prop somebody.

In phrases

prop up (v.) (UK Und.)

to arrange, to suggest, to fabricate a story.

[UK]Thieves Slang ms list from District Police Training Centre, Ryton-on-Dunsmore, Warwicks 8: Prop-up: To suggest a case or give information to the police.
[UK]D. Powis Signs of Crime 197: Prop Up, to Originally and most commonly short for ‘proposition’. Still used in that sense but also to suggest or arrange, particularly through a third person: ‘we must prop up a story over this.’.