>Beyond the facts corrected by other user, graemep, the translator school was in fact established after the christian kingdom of Castile conquer the city of Toledo, and the king Alfonso X [1].
I have replied to the other users comments, please check them out.
The Toledan school/library/knowledge centers were not established by king Alfonso, it was continued by him when he captured Toledo from the Islamic Spain Empire in 11th CE [1]. Case in point, the venerable and infamous Toledan Tables were compiled in the 11th century (around 1080) by a group of Arabic astronomers in Toledo, Spain (Al-Andalus), led by the renowned astronomer Abū Ishāq Ibrāhīm al-Zarqālī (known in Latin as Arzachel). They were essentially the Zij of Toledo, drawing heavily on earlier zijat from the Islamic world, like those of al-Khwarizmi and al-Battani [2].
The Andalusian parts, however, continue under the muslim rule for several centuries until the genocide and the ethnic cleansing of the muslim and the jews during the final phase of Reconquista in the 15th CE. It ended nearly 800 years of muslim era in Spain which is so far longer than European have been in the American continents [3].
Credit to the Spanish and the European when they make the most of the capture of Toledo centers with all the translated and original books, thus kickstarted the Renaissance age, since before they were in the dark ages [4].
Another fun facts, the Almagest version of the Galileo notes in the OP article is the Latin translation of Almagest by Gerard of Cremona in Toledo around 1175, from the Arabic translation of Almagest performed in the House of Wisdom (or Baitul Hikmah). This makes Al-Ma'mun the patron of the Almagest mentioned the OP article [5].
[1] Reconquista:
https://en.wikipedia.org/wiki/Reconquista
[2] Toledan Tables:
https://en.wikipedia.org/wiki/Toledan_Tables
[3] Siege of Toledo (1085):
https://en.wikipedia.org/wiki/Siege_of_Toledo_(1085)
[4] Dark Ages:
https://en.wikipedia.org/wiki/Dark_Ages_(historiography)
[5] House of Wisdom: