How to record a private medical insurance for one employee ( account) and the owner has to withhold anything or the third party HR company we work with has to do it ?

As long as the assistant is an employee and the employer is paying the cost of the employee's health insurance, the premiums paid are not subject to any payroll taxes.  Therefore, it does not need to go through the HR company.  However, if the owner is a >2% S-Corp shareholder, then that amount should go through the HR company as it should be reported on the owner's W-2 as wages.  Here's what the IRS says:

If an employer pays the cost of an accident or health insurance plan for his/her employees (including an employee's spouse and dependents), then the employer's payments are not wages and are not subject to social security, Medicare, and FUTA taxes, or federal income tax withholding. Generally, this exclusion also applies to qualified long-term care insurance contracts. However, the cost of health insurance benefits must be included in the wages of S corporation employees who own more than two percent of the S corporation (two percent shareholders).