one way is to make sure the STF is set to tracking mode (check mark highlighted) then make sure the image you've applied an STF to is foregrounded (blue titlebar).
then, with the HistogramTransformation process window open, drag the triangle (at the bottom left of the STF window) to the bar containing the triangle of the HistogramTransformation window. that copies the stretch from the STF to the HT process.
then apply the HT process to the window in question, either by clicking the square button in the bottom toolbar of HT, or dragging HT's triangle to the image.
at that point your image will likely turn white, because now it's stretched + the original STF is still applied. when you turn off the STF on the image, it should look like it did before, but now the stretch is "real". when you save it and open in another program, it will look like you expect it to.
rob