Is it permissible for a Christian, being convinced of Islam and having decided to embrace it, to marry a Muslim woman? How can I help him?
To be a Muslim, must he read and be convinced of the whole of the Quran, or just utter the testimony: La Ilaaha Illallaah (There is none worthy of worship except Allaah). Please note that he is Spanish and his cultural background affects his understanding of what he reads.

All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and messenger.

Once a disbeliever embraces Islam he becomes a Muslim, ordered to fulfil the same obligations as all Muslims and eligible for the same rights. Thus, this man is not to be deprived from marrying a Muslim woman, provided that the considerable conditions and pillars of marriage are fulfilled.

A disbeliever becomes a Muslim when he/she utters The Two Testimonies of Faith, performs prayers, pays Zakah and believes in all the other pillars of Islam. Ibn ‘Umar quoted the Prophet as saying that Allaah ordered him to fight people until they say: La Ilaaha Illallaah, Muhammad Rasoolullaah (I testify that there is none worthy of worship except Allaah, and that Muhammad is His messenger), perform prayers and pay the Zakah. Whoever does so will have his property and life protected, unless he does something that makes him deserving of death (as a penalty), and his final reckoning will be with Allaah. [Al-Bukhari and Muslim]

He does not have to read the whole of the Quran; however he must memorize the required chapters for his prayers to be valid, i.e. Al-Faatihah. (first Chapter of the Quran) Nevertheless, he has to believe in the Quran as a whole: in all of its chapters, verses, and letters, without denying a single letter, because every single letter is from Allaah.

If the questioner is a man who can teach the convert the pillars and obligations of Islam gradually, beginning with the points of paramount importance in a simple and convincing style, do it. Otherwise, refer the man to a scholar to do this job. In both cases you will be rewarded, Allaah willing. The one who guides others to good deeds will receive the same reward they get. 

However, if the questioner is a woman, then you must let a man teach the convert. You must not do it yourself, lest an Islamic violation results, such as being alone in seclusion with the convert or speaking to him softly, or similar violations.