Can I open an HSA mid-year after switching jobs if I had an FSA with my previous employer (funds fully used, no COBRA)?

I changed employers mid-year. I had an FSA account and now I would like to open an HSA account with the new employer. This would happen in the same fiscal year. The FSA funds have been used already. I also understand that my new employer funds a small amount of the HSA on my behalf. Even if I don't open the HSA account myself, am I allowed to have it via my employer funding it on my behalf? Thanks!

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