Is it permissible for a Muslim to pray Fajr after sunrise if he is unable to stop to pray it on time due to the nature of his work as a truck driver?

It is not permissible to offer the prayer before its prescribed time nor to delay it beyond it. Whoever offers it before its time, it is not valid for him by consensus. And whoever delays it beyond its prescribed time without an excuse commits a grave sin, for Allah has condemned those who delay prayers from their times. Therefore, the driver should perform ablution and pray Fajr at its time, unless he fears for himself or his property, in which case he is permitted to pray in his current state and to the best of his ability.