shared service structure, Requisition BU is the only one available in Bill-to BU in Site assignment

We configured service provider for between 2 BU to produce the following (each BU has its own Ledger)
BU01 : Should be solely responsible for the requisition
BU02 : Should be responsible for PO creation, invoice processing, and payment.

we have configured service provider relations between the 2 BU
Payables Payment Service Provider & Procurement Service Provider Set to BU02

when we created the supplier, the Procurement BU was BU02, and the client BU was BU01, but in the Bill-to BU only BU01 was available that resulted in the invoice BU be BU01 and not BU02
any recommendation will be appreciated

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Attachment

1- Supplier Site assignment