I found many references to "present truth" as far back as Russell's time but none saying "current truth" not that elders might independently use that phrase.
Revelation book chapter 1 p8 (on most recent WOL online)
An even stronger reason for publishing this book is the need to keep up-to-date with present truth. Jehovah is continually shedding greater light on the meaning of his Word, and we can expect that our understanding of Revelation, along with other prophecies, will be sharpened as we draw closer to the great tribulation. (Matthew 24:21; Revelation 7:14) It is important that we be well informed. As the apostle Peter wrote concerning divine prophecy: “You are doing well in paying attention to it as to a lamp shining in a dark place, until day dawns and a daystar rises, in your hearts.”—2 Peter 1:19.