I don't have any experience with adding a SSD to an AIO, but I'll bet that it can be done. I know there are several AIO's that can be configured with a SSD. Here is a guide that shows how to replace the hard drive. I suggest opening the case to check how the HDD is installed. Then, you will have an idea if there is a way to get the SSD to work. I am certain that you will need an adapter to make the 2.5" SSD fit properly in the enclosure that is used. I checked Crucial Memory's website to see if they have SSD's that they recommend and there were none.
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I am not an HP Employee!! Intelligence is God given. Wisdom is the sum of our mistakes!!