Sure, the H9 has a preset list on it with 99 presets. When you buy a new algorithm, it doesn't place any of its presets in the list of 99 presets on the H9 itself, because it could be that user has carefully ordered that preset list for an upcoming live performance or something along those lines.
So, after you purchase an algorithm, you can use it on the H9 itself by pressing the preset button twice and cycling to the algorithm name. You can also use all of the algorithm's presets from inside H9 Control, and you can save these presets from H9 Control to the preset list on the H9 if you wish.
