Is it ok to have FSA & HSA in the same calendar year with the different employer?

I was with the employer 1 from Jan - May where I enrolled for Healthcare FSA for $500. I had some $250 rolled over from last year FSA as well. During the employer, I hardly used the FSA around $50. Because of the immigration issues, I was moved out of the employer1(loss of employment), even I was out of the country for 2 months. My FSA contributions are also not accessible after the moving out from the employer, and last around $700. I joined the employer 2 in August, the new employer is providing good HSA options.

Is it ok to enroll HSA with the new employer since there is no monthly overlapping on FSA & HSA. Going back to my original question, is it ok to have FSA & HSA in the same calendar year with the different employer in the event of employment loss?