His moniker is often mistakenly written as «Kulal». This individual and the circumstances of his mausoleum's construction are reported by one of the historians of Amir Temur and the first Temurids, Sharaph ad-din 'Ali Yazdi. According to him, sheikh was a spiritual advisor (pir) to Amir Taragai, the father of Amir Temur, who also deeply respected that elder. Amir Taragai took part in meetings with Shams addin Kular and expressed his respect to him. According to Yazdi, his family could trace its roots back to the famous Sufi sheikh Shikhab ad-din Abu Khafs 'Umar Sukhravardi (1145–1234). This Sufi sheikh did not support the practice of long fasts (chillanishin) and seclusion. He maintained contacts with those in power, believing that this would help them follow Shari'a norms. It is known that he carried out diplomatic assignments for Caliph an-Nasir, for example, going to negotiate with Khorezmshah Muhammad Tekesh (1200–1220).
After his death from illness in the year 762/1360–61, Amir Taragai was buried in Kesh, next to his father Amir Barkul and other relatives. As soon as Amir Temur took the throne (1370), he ordered that the remains of his father (in 775/1373–74) be taken to the tomb of Shams ad-din Kular and that a dome construction be built there (evidently on top of the tombs of the sheikh and his father). It was located not far from the Cathedral Mosque. The same author mentions the tomb of Shams ad-din Kular and the constructed complex in connection with the fact that the body of Amir-zade 'Umar-sheikh, who was killed during the siege of a tower, was taken to Kesh (killed in 796/1394; the body was transferred in 797/1395).
In this fragment the author describes the complex in detail and writes that he was buried in «a building that was among the rebuilt constructions of Sakhibkaran.» He adds that it was located in the area (be-makhalli) «from the qibla side» (to the west) from the Shams ad-din Kular and Amir Timur mausoleum (mazar). To the right and to the left of the new mausoleum of Amir Temur's elder son, Mirza Jahangir (d. 1376), «new tombs and open fenced mausoleums» were constructed. Amir Temur ordered that all his relatives and descendants be buried there, wherever they might die.
He should not be confused with his namesake Shams ad-din Kulal (d. 1370), who was one of the teachers of the famous Sufi sheikh Baha' ad-din Muhammad ibn Burhan ad-din Naqshband (1318–1389). Naqshbandi hagiography artificially linked the names of Amir Temur and Shams ad-din Kulal (d. 1370) on the basis of legends (perhaps appealing to the similarity of his name with Shams ad-din Kular) that Sahibkiran allegedly received blessings from this sheikh.
You can learn more about the topic in the book-album "Architectural epigraphy of Uzbekistan. Qashqadaryo, Shahrisabz" of the series "Architectural epigraphy of Uzbekistan".