USCIS announced a press release today saying that they plan to open up the premium processing for H1B Applications filed with USCIS in phases. They plan to do it in phases to catch up with the demand. As you all know, they have suspended the premium processing due to the Corona Virus situation.
H1B petitions filed before June 8th, 2020
If you have filed an H1B petition before June 8th, 2020 as cap exempt such as transfers, extension or amendment, including the universities, non-profit research institutions, then you can file premium processing for the same petitions that are pending with USCIS from June 8th, 2020. All you need to do file form I-907and upgrade your petition or request premium processing for the same.
Premium Processing from June 15th for H1B Cap Exempt Employers
Starting from June 15th, 2020, cap exempt employers such as the higher education and nonprofit research insitituionts can file H1B premium processing for their new H1B petitions concurrently.
H1B 2020, 2021 Cap Subject Petitions, New H1B petitions
Starting from June 22nd, you can upgrade all the H1B 2021 cap subject petitions, including those from previous cap like FY 2020 or before to premium processing. Also, it applies to both Change of status and consular processing petitions.
Also, starting from June 22dnd, you can file H1B petitions along with premium processing concurrently.
H1B premium processing is a big deal for many waiting for decisions as it lets them plan their immigration status in US. You can check the USCIS official alert for more info.