GA instructor reported that student pilot VFR solo cross country training flight had a radio malfunction which resulted in descending to a low altitude to stay below the clouds. The instructor indicated the student did not maintain communication with ATC; then diverted to a non-towered airport and landed safely.

Narrative

A student pilot endorsed by the instructor pilot filing this report; received a possible pilot deviation from Florence Tower due to the inability to establish positive two-way radio communications prior to entering Class D airspace.The student pilot was endorsed for a cross country solo along the direct route from ZZZ to FLO; then ZZZ1 and returning to ZZZ. The student pilot arrived at ZZZ at XA:05; and reviewed the route; flight plan; and weather situation with the instructor pilot. The instructor pilot endorsed the student pilot's logbook; and provided instruction to the student pilot for strict details for today's flight. Among that instruction included receiving a VFR flight following from Charleston Approach; reviewing ATC clearances (common phraseology such as traffic advisories; left & right downwind; & cleared for the option); and potential weather issues that may arise (such as advection fog / low level clouds common for the morning flight block. Not forecasted; yet had been a recent trend for early mornings along the coast). Strict guidance was given to NOT descend below 1;000 AGL if clouds were low lying; and to return to ZZZ above the cloud layer and await further instruction from instructor pilot. At XA:13; instructor pilot made a courtesy call to Florence Tower ATC via the Clearance Delivery phone number advising that the student solo would be arriving at FLO after XB:15. The Tower controller asked the instructor pilot questions; such as; 'Is it there first solo; & how do you think the student will do?' The instructor responded; 'I think they will do well. They have been to Florence 2-3 times recently; and performed well. It is their first XC solo.' The instructor pilot gave the Florence Tower their phone number to call if issues arose. At XB:06; the student pilot departed solo from ZZZ & made departure radio calls accordingly on the correct frequency. At some point in flight; the student pilot was experiencing radio issues that restricted their ability to receive communications. At approximately XB:46; the student pilot (SP) sent a text message in-flight to the instructor pilot (IP) noting that 'No one [was] answering [her/him] on the radio.' Instructor pilot responded via text message at XB:47; 'For ZZZ?' SP responded; 'Florence'. IP responded; '125.1 tuned?' SP responded; 'Yes.' IP responded; 'Radio turned up? Is it on Comm 1? Were you talking to Approach?' SP responded; 'I tried but no one was talking.' IP responded; 'Don't go below 3;000 [feet MSL]. Tune in 123.05 real quick and let me know if you hear me.' SP responded; 'I'm tuned in.' IP responded; 'Unplug your headset and plug it back in.' SP responded; 'Done.' IP responded; 'I can hear you. Make sure your volume is up on the plane. Push the Comm knob in and turn up the volume.' SP responded; 'Ok.' IP responded; 'Avionics master on?' SP responded; 'Yes.' IP responded; 'Try tuning and talking on Comm 2?' SP responded; 'Done.' IP responded; 'I'm trying to get a hold of you. Go to ZZZ1 & land. Call me on the ground.' SP responded; 'Ok.' IP responded; 'Call flight school dispatcher when you're on the ground. I might head that way in my next block.' Student pilot reported that they were on the ground at ZZZ1 at XC:23.At XC:35; the instructor pilot returned a phone call from a manager at the Florence Tower; who informed the instructor pilot that the student pilot had received a possible pilot deviation due to the inability to establish positive two-way radio communications. After a detailed discussion between the instructor pilot and controller; we learned that the student pilot had attempted to make radio calls and was heard by the Tower; but was not receiving the Tower's transmissions. There was a scattered layer at about 1;200 feet and the student descended below the clouds; down as low as 500 feet MSL to stay beneath them. The tower mentioned the student pilot had climbed above the layer and entered the airspace; but did not affect operations or any other aircraft. The Tower suggested that the student pilot should have squawked 7600 for loss of radios; however; the student was directed by instructor pilot to return for landing at ZZZ1 so as to avoid an emergency situation affecting the operations at FLO.The student pilot made questionable decisions; even going against instructor instruction during the pre-flight brief to stay above the clouds & above 1;000 AGL if clouds became an issue. Additionally; he did not follow instruction to establish a flight following from Charleston. He should have informed instructor pilot much earlier in the flight; as he knew the instructor pilot had a radio available; yet continued onward anyways. Overall; this was the result of either lack of judgement on the student pilot's part; or lack of training from instructor pilot in previous lessons for radio failure emergencies; or a combination thereof.