ANA - early June (after completing test flights and pilot training)
Air India - around mid May
Ethiopian - April 27
JAL - early June (after completing test flights and pilot training)
LAN - unknown
LOT Polish Airlines - June 5
Qatar Airways - end of April
United Airlines - May 31st but may be able to restart earlier
Today the amended Airworthiness Directive was posted in the Federal Register thus making the FAA's certification of the battery fix official. Any US registered 787 can now fly with the battery fix. Already Japan and Europe has followed the FAA's lead on this as has approved of Boeing's fix though I also expect that India, Ethiopia, Chile and Qatar will all follow suit fairly quickly. The first set of 787s should be completed by now. LOT Polish Airlines is (or already has) ferrying its 787 stranded in Chicago to Addis Ababa where a Boeing team is there to install the battery fix on the 4 aircraft belonging to Ethiopian. Word is that LOT's second aircraft, which is currently in Warsaw, will also be flown to Ethiopia for the fix. Qatar 787 that was stranded at London Heathrow was ferried back to Doha for the fix and one United jet at LA was ferried to San Antonio, Tx. for the repairs.
Given Japan's approval of Boeing's fix, ANA announced that starting this Sunday, May 28th, their 787s will fly about 230 test flights in order to re-train their team of 787 pilots as well as reassure their passengers that the airplane is safe to fly one. They plan on resuming regular passenger service in June. ANA is also looking to see a resumption of 787 deliveries with ZA512 (LN 82, JA818A) being the first 787 to be delivered since the grounding in January. It can be delivered as early as late next week but ANA pilots still have to fly the customer flights on this airplane.
Outside of this one pending delivery, I can see LOT Polish, Air India, JAL and even China Southern and Hainan taking deliveries in May. In June we can see deliveries to Thomson, Qatar, JAL, ANA and ILFC being made. I do expect that Boeing will now be aggressive in their production flight test program as they need to clear the inventory sitting at Everett and Charleston.
Lastly, a reader sent me this link to a video from the BBC detailing the 787 battery fix work that is going on in Ethiopia.