Can I still find out that my mother didn't have a criminal certificate in the mainland before she took her Hong Kong identity card with her?

If your mother is over 60 years old and has no other children in Hong Kong, you can apply for a one-way permit to settle in Hong Kong on the grounds of caring for your parents.

Your mother must be a non-permanent resident at present. If she goes on a one-way permit, there will be no problem. At that time, your father can also apply to settle in Hong Kong on the grounds that the elderly do not take refuge in their relatives.

If your mother didn't go with a one-way permit, I'm afraid it would be a little difficult, because the mainland account has not been cancelled at this time. To apply for relatives' asylum immigrants, Hong Kong residents' Home Visit Permit is required. Non-permanent residents can only apply for a home visit permit immediately if they go there with a one-way permit, while those without a one-way permit can only apply seven years after they become permanent residents.