I have never heard of a Checking Suspense Account attached to an HSA so I can't answer your question. Sounds like you may have a cobbled together program if you have to run transactions through multiple accounts to post transactions. Do your agreements cover this process? What is the base account? A savings account? If so and you are eventually posting checks and debit card transactions to the savings account by running them first through a shadow checking account, you most likely are going to run afoul of the Reg. D savings account transaction limitations.
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