She has become Muslim and he wants to marry her but his mother refuses

We suggest that you should continue in your attempt to convince your mother to accept your marriage to this girl. If she insists on refusing then it is good for you to obey your mother and do as she wishes. There are many women and a man does not have to marry a particular woman. So obedience to your mother should take precedence in this case, because that means that you will be honouring her and treating her kindly. Allaah says (interpretation of the meaning): 

“And your Lord has decreed that you worship none but Him. And that you be dutiful to your parents. If one of them or both of them attain old age in your life, say not to them a word of disrespect, nor shout at them but address them in terms of honour”

[al-Isra’ 17:23]

Ahmad (15577) narrated that Mu’aawiyah ibn Jaahimah came to the Messenger of Allaah (peace and blessings of Allaah be upon him) and said: “O Messenger of Allaah, I want to go and fight (in jihad) and I have come to consult you.” He said, “Do you have a mother?” He said, “Yes.” He said, “Stay with her for Paradise is at her feet.” 

Shaykh Shu’ayb al-Arna’oot said: its isnaad is hasan. 

It was also narrated by Ibn Maajah (2781) as follows: “I went to the Messenger of Allaah (peace and blessings of Allaah be upon him) and said, ‘O Messenger of Allaah, I want to go for jihad with you, seeking thereby the Face of Allaah and the Hereafter.’ He said, ‘Woe to you! Is your mother still alive?’  I said, ‘Yes.’ He said, ‘Go back and honour her.’ Then I approached him from the other side and said: ‘O Messenger of Allaah, I want to go for jihad with you, seeking thereby the Face of Allaah and the Hereafter.’ He said, ‘Woe to you! Is your mother still alive?’  I said, ‘Yes.’ He said, ‘Go back and honour her.’ Then I approached him from in front and said, ‘O Messenger of Allaah, I want to go for jihad with you, seeking thereby the Face of Allaah and the Hereafter.’ He said, ‘Woe to you! Is your mother still alive?’  I said, ‘Yes.’ He said, ‘Woe to you! Stay by her feet, for Paradise is there.’” This hadeeth was classed as saheeh by al-Albaani in Saheeh Sunan Ibn Maajah. 

Ibn Abi Shaybah narrated in his Musannaf that Abu Talhah al-Asadi said: I was sitting with Ibn ‘Abbaas and two Bedouins came to him and spoke with him. One of them said: “I was looking for a camel of mine and I stayed with some people. I liked a girl of theirs so I married her, and my parents swore that they would never accept her. I swore that I would free a thousand slaves give one thousand gifts and slaughter one thousand camels if I divorced her.” Ibn ‘Abbaas said: “I am not going to tell you to divorce your wife or to disobey your parents.” He said, “What should I do with this woman?” He said: “Honour your parents.” 

Something similar was narrated from Abu’l-Darda’. If this had to do with divorcing a woman after marrying her, it is more apt that you should obey your mother before marriage takes place. 

And Allaah knows best.