Twitter question

I set up a Twitter feed for my employer. I can access the account from the iMac desktop at work and from my Windows machine at home. My boss cannot log into the account from his Mac laptop, no matter how he tries.

I logged out of the account on the iMac to let him log in, without any luck. Then, when I logged in again, I had to type in a captcha to be allowed back in, which I had not needed to do previously.

Twitter tech support is not helpful, they want to reset the password, and I'm not sure that'll fix the issue.

Thoughts?