One doesn't "convert" a S-Corp to an LLC.

Your client has a dissolution, with the assets distributed (at fair market value) to the shareholder(s) AND any resultant gains reported/taxes paid.

Then the assets (some, or all) are contributed to the LLC, as well as (possibly) any associated liabilities.

Off the top of my head.. but I'm thinking a new FEIN is required (unless it's a SMLLC without payroll).