Relatives immigrated to the United States after obtaining permanent resident status in Hong Kong, and now they want to do business with Hong Kong identity cards. Is there a problem?

No problem. Both Hong Kong and the United States default to dual citizenship, which is default, not recognition! This is internationally recognized.

Moreover, American citizenship has a limit of stay in the Mainland, while Hong Kong identity cards (or home visit permits) can be said to have no limit of stay (as long as they are within the validity period, the validity period of home visit permits is 10 year).

Therefore, it is absolutely no problem to handle business in the mainland as Hong Kong!