Sorry but NO EMPLOYER no matter who they are can get a refund of the employer portion of the FICA taxes they pay for any employee. There is no way to do it ... the SSA/Medicare systems get to keep what you may think is excess but it is not. All employers must pay the employer's portion of the FICA taxes until that employee reaches the max for the year for THAT employer. The fact that the employee had other wages from other employers is immaterial. Only the employee has a way to get the excess withholding refunded ... the employers do not.
Read the form and the instructions :
5a. Taxable social security wages. Enter the total wages,
including qualified sick leave wages and qualified family
leave wages paid this quarter of 2022 for leave taken after
March 31, 2021, and before October 1, 2021; sick pay; and
taxable fringe benefits subject to social security taxes you
paid to your employees during the quarter. Don't include the
qualified sick leave wages paid this quarter of 2022 that are
reported on line 5a(i) or qualified family leave wages paid this
quarter of 2022 that are reported on line 5a(ii) for leave taken
after March 31, 2020, and before April 1, 2021. For this
purpose, sick pay includes payments made by an insurance
company to your employees for which you received timely
notice from the insurance company. See section 6 of Pub.
15-A for more information about sick pay reporting. See the
instructions for line 8 for an adjustment that you may need to
make on Form 941 for sick pay.
Enter the amount before payroll deductions. Don't include
tips on this line. For information on types of wages subject to
social security taxes, see section 5 of Pub. 15.
For 2022, the rate of social security tax on taxable wages,
except for qualified sick leave wages and qualified family
leave wages paid in 2022 for leave taken after March 31,
2020, and before April 1, 2021, is 6.2% (0.062) each for the
employer and employee or 12.4% (0.124) for both. Stop
paying social security tax on and entering an employee's
wages on line 5a when the employee's taxable wages,
including qualified sick leave wages paid in 2022 that are
reported on line 5a(i), qualified family leave wages paid in
2022 that are reported on line 5a(ii), and tips, reach $147,000
for the year. However, continue to withhold income and
Medicare taxes for the whole year on all wages, including
qualified sick leave wages paid in 2022, qualified family leave
wages paid in 2022, and tips, even when the social security
wage base of $147,000 has been reached.
https://www.irs.gov/pub/irs-pdf/f941.pdf
https://www.irs.gov/pub/irs-pdf/i941.pdf
