You will need to create a separate invoice to the Destination store based off the order that the Destination store has sent to you to fulfill. How payment is arranged and to what timeframe is up to you and the Destination store to agree on.
To help keep track, your Destination store partner can use the Payouts add-on (Shopify only) to set commissions and create payout records that you can review in your Syncio app. Payouts doesn’t move money, so payment is still arranged between the two stores. Learn more: Payouts Add-on - Source store side