The whole width of the puzzle is just enough to fit the four letters upright (putting any of them sideways won't work). The problem is the last 2 x 1 piece. This must go in the gap between two letters somehow.
Observe that for the white squares to stay contiguous, the I must be the second letter. It can't fit in the third space, and if it were in the first or fourth then it would close off a set of white squares.
With the I in place, we conjecture that the concave shape of the I's sides will permit the fitting of the 2 x 1 piece, combined with the empty space in the bottom half of the F. A quick thought confirms that the 2 x 1 piece cannot possibly fit between any other two letters. After trying to unsuccessfully fit the F in the leftmost spot such that there is room for the 2 x 1 piece, we can deduce that the F must be in the third place, to the immediate right of the I. We can find the correct placement of the F and the 2 x 1 piece from there. The rest is trivial.