Is it permissible for my friend to wear the hijab and pray Jumu'ah with the intention of attending a lesson at the mosque, then take it off and discontinue her prayers? And is my companionship with her permissible if she does not pray at all?

There is no doubt that abandoning the hijab (definition) is one of the abominations that a Muslim woman must forsake, as Allah (the Most High) says: "O Prophet, tell your wives and your daughters and the women of the believers to bring down over themselves [part] of their outer garments." And abandoning prayer is a greater حرمة (prohibition/sacredness), as the Prophet (peace and blessings be upon him) said: "Indeed, between a man and polytheism and disbelief is the abandonment of prayer." A Muslim woman must hasten to rescue her friend, be patient in doing so, and seek help from Allah, for the Prophet (peace and blessings be upon him) said: "That Allah guides through you one man is better for you than red camels." It is wise to gradually advise her and invite her with wisdom and good counsel, encouraging her to attend lessons in the mosque and the Friday sermon, and to perform prayer. If she tastes the sweetness of faith, she will not return to what she was doing. Do not resort to abandoning her until you despair of her accepting the truth. It must be known that the hijab that covers the entire body of a woman, except for the face and hands, is a condition for the validity of prayer.