Joe F. answered 01/09/21
Patient and Knowledgeable Music Theory Instructor
The inversion doesn't matter so much, as it won't change the sound of the chord fundamentally. You need to look at the context of where the augmented chord is introduced: which chord proceeds it, and which chord follows it? How are these chords voiced? You would probably choose the inversion of the augmented chord based what ever motion would give your the smoothest transition between chords.