Jehovah's Witnesses believe that only 144000 (the group mentioned in Revelation 14:1-3) have a heavenly hope, while the rest of humankind have the hope of living forever on earth. This is for example explained in the selected answer to this question.
Additionally an answer to this other question says (emphasis added):
However, all of these faithful ones from before Jesus' day have the earthly hope, just as most Jehovah's Witnesses have today. The heavenly hope has been reserved for 144,000 which have been chosen by Christ ever since his death. Those with the heavenly hope will assist Christ in ruling the righteous ones on Earth.
This is the only distinction between those who died before Jesus' death and those who died after: the ones who died after are able to be members of the 144,000.
However 2 Kings 2:11 says that Elijah was taken to heaven:
And it came to pass, as they still went on, and talked, that, behold, there appeared a chariot of fire, and horses of fire, and parted them both asunder; and Elijah went up by a whirlwind into heaven.
How do Jehovah's Witnesses view the case of Elijah if only those who died after Jesus' death are among the ones that go to heaven?