The HSA belongs to you, not to the employer. Like an IRA, you can take it with you when you change jobs.
The employer is actually providing HDHP insurance coverage (High Deductible Health Plan), not the HSA, which is normally provided by a third-party financial institution. Yes, the employer may help you set up the HSA, but you don't have to make a new one if you already have one.
You will have to tell your employer the name of the HSA administrator (the financial institution you have been using) and the HSA account number so that they can deposit their contributions and your contribution via payroll deduction into the correct account.
Otherwise, just continue using the HSA and making payments as you have before.
