The original seller in the first Salam cannot be made the buyer in the parallel contract. That would create a buy-back arrangement.
The source also treats a wholly owned subsidiary of the first seller as effectively the same party for this purpose. Partial common ownership is treated differently from complete ownership.
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Parallel Salam (السلم الموازي): Two Independent Contracts
The original seller in the first Salam cannot be made the buyer in the parallel contract. That would create a buy-back arrangement.
The source also treats a wholly owned subsidiary of the first seller as effectively the same party for this purpose. Partial common ownership is treated differently from complete ownership.