I would split the fairing, put a Ferrite bead over the power supply as close to the lighter plug as possible, you can slip one over ground also and try that first. cheap
If that doesn't work what is happening is that it the phone or device is getting it's ground from a different location than the radio, but the radio is pulling the ground from the device instead of the intended ground or the grounds are out of phase. If you make the grounding point the same and have the same length wire that is one fix. Ferrite bead may help but I suspect it is the power supply from your lighter to your phone. You could also try a new power wire from the lighter.