Yes, they can merge and elect to be a single s-corporation
The owner of the c-corp can change to an s-corp and then it's a simple matter of exchanging shares for ownership in the ending entity as per their desires.
Form 2553 must be signed and dated by the president, vice president, treasurer, assistant treasurer, chief accounting officer, or any other corporate officer (such as tax officer) authorized to sign. If Form 2553 is not signed, it will not be considered timely filed.
Required form to be filed to change filing status:
Step 1. Timely file a paper copy of the Form 2553 with the appropriate Service Center as directed in the Form 2553 instructions. You may mail or fax this form.
Step 2. The corporation will receive an acknowledgement and approval of the S corporation election. If the notification of approval is not received, the corporation should follow-up with the Service Center where the Form 2553 was filed.
Step 3. File the last C Corporation return (Form 1120) by the due date or extended due date. Note: Some taxpayers are required to file electronically. For additional information on which Form 1120 filers are required to file electronically, please see T.D. 9363, I.R.B. 2007-49.
Step 4. File the S Corporation return (Form 1120S) by the due or extended due date. Note: Some taxpayers are required to file electronically. For additional information on which Form 1120S filers are required to file electronically, please see T.D. 9363, I.R.B. 2007-49.
The filing of the initial Form 1120S return will finalize the change of the entity’s filing requirement on the Internal Revenue Service’s records.