Is it permissible to pray on behalf of someone who does not pray?

Praise be to Allah.

Prayer is one of the pillars of Islam and it is not valid except when done by the one who is obliged to do it. Not praying is kufr which puts a person beyond the pale of Islam; see question no. 2182. It is not permissible for you to offer prayers on behalf of someone else who does not pray. This ruling is one upon which there is consensus and there is no difference of opinion among the scholars. 

Ibn Qudaamah said: “The visible acts of worship such as prayer, fasting, purifying oneself (wudoo’) cannot be delegated to others because they have to do with the body of the person who is obliged to do them, so no one else can take his place, except in the case of a vowed fast, which a person may do on behalf of one who has died, but this cannot be done by way of delegation. 

Al-Mughni, 5/207 

You have to keep on advising this person to pray, and encouraging him and warning him. May Allaah open his heart to beneficial words. 

And Allaah knows best.