MY sons A/C outside fan stops running yesterday. Here in GA it was hot as Obama. Having a rental unit not in use and it being Sunday I removed the capicitor from the rental unit's A/C. However it was a 440 VAC 60 Hz the originl was a 370 VAC 50-60 Hz. My question although the capacitor worked and the A/C is working will it damage anything.

The value in uF should be the same, higher working voltage generally increases reliability and cost for a first order reason. So, it won't harm anything.

I disagree with your Obama reference, but your cap will work fine