What is the ruling on settling Al Rajhi Bank's debt through Bank Albilad using the aforementioned mechanism?

There is no objection to taking this path to settle the debt. The transaction is based on two matters: First, Murabaha (cost-plus financing) in shares, which means that Bank Albilad sells to you, on an installment basis, the shares you choose after it acquires ownership of them. This is permissible, provided that the shares are sharia-compliant, like those of Al Rajhi, Albilad, and Alinma. Second, Tawarruq (monetization) in shares, which means your purchase of shares with the aim of selling them to obtain cash. This is permissible, provided that the shares enter your portfolio and then you sell them yourself. Once the shares are sold and you receive the cash, you can settle your debt, while committing to pay the installment price of the shares to Bank Albilad.