Premium processing for FY2020 cap-subject H-1B petitioners requesting a change of status on Form I-129 will begin on 5/20/19. For all other FY2020 H-1B cap-subject petitions, it will begin in June 2019 or later. From 5/20/19 until 6/3/19, final notices will not be sent using prepaid mailers.  

Read the USCIS news release.