The transfer is made at the client's instruction1. OSTTRA calls the receiving broker a Prime Broker. In OSTTRA's description, the executing broker or investment manager sends the trade details to the receiving party, which matches them, and a confirmation returns when they match2.
Consider a hypothetical example in which Company J, an asset manager, has a trade executed at Bank K and instructs that it be turned over to Bank L. The trade then moves to Bank L. The transfer from Bank K to Bank L is the give-up. Splitting the trade across Company J's accounts is allocation. OSTTRA's materials describe both a form that sends block-level and allocation-level details to the receiving party and a form that allocates through give-ups. Which of allocation and give-up comes first is not fixed.