Converting to Materia, and Desynthesis, are two very different things.

For Materia Conversion, combat gear will have a small chance of getting you the Materia you want. Quickarm is Skill Speed, right? Stay away from the DoM gear.

For Desynthesis, one specific fish will give you a Quickarm Materia .. but I don't know which fish. It should be an ARR green fish though.