I maxed out on Social Security tax earlier this year from stock option exercises and restricted stock vesting at my prior company. Then I changed jobs. Why did my new employer withhold Social Security tax from my wages?
The Social Security withholding by the prior employer does not matter to your new employer. Every company must withhold Social Security tax without considering what an employee's prior company withheld. This can result in Social Security withholding beyond the annual income ceiling ($128,400 in 2018).
To find out how you can recover the excess amount, and whether you can arrange this as a tax credit or as a refund, see the FAQ on that topic.