Switching to HDHP with HSA

I am switching employers this year and will be moving from a standard PPO healthcare plan with FSA to a HDHP with HSA and my new employer will make contributions to the HSA. There will be some overlap where I am covered by both plans. I know while I am still covered by the FSA I am not eligible to contribute to the HSA. However, can my employer contribute to my HSA while I am ineligible, as long as I don’t use the HSA, or will they have to wait until I am eligible for an HSA to begin contributing along with my contributions?

 

Thanks!