It means "major seventh". "Fj" is equivalent to "FMaj7" or "FΔ7". It is rarely used.
A clue to its meaning is given a few bars later, in the final measure of the piece. The trumpets are playing their A and E, respectively, with "Fj" indicated as the chord. E being the major seventh of F, it's clear the chord would be a major seventh chord.
An even more clear example can be found on page 20 of the same book. As shown below, there is a progression "Dm Dmj Dm7". The second trumpet plays D, Db (C#), C respective to each chord symbol. In other words, the basic chord is D minor, with the second trumpet making a chromatic decent from ^8 to ^#7 to ^7. Thus, Dmj is D minor with a major seventh, or DmM7.