To what extent is consent required when referring health checkup follow-up patients to an EAP?

Hello. I am in charge of health and safety at the workplace.
There is an employee among the follow-up care recipients after the health checkup who wants to receive counseling due to stress or sleep problems, so I would like to introduce them to the EAP.
I don't think there would be a big problem if you just explain the EAP application method to the staff and have them apply themselves.
I would like to know if separate consent is required when a health manager shares employee information with an EAP coordinator or counseling agency for referral.

In particular, since transmitting health checkup results or information confirmed during follow-up care to the counseling agency involves health information, I am concerned that it might not be appropriate to process it together with the existing checkup consent.
Cases where only the employee's name and contact information are provided for the counseling agency to contact them, and
Do I need to use a different consent method if I also share test results or current symptoms?

If possible, I would like to link the information so that the staff does not have to explain the same thing again, but it is unclear how much I can convey due to privacy concerns.
I am curious to know how places that have referred patients for EAP counseling during health checkup follow-up care typically obtain consent and operate.