Did the Qarmatians steal the Black Stone, break off a piece of it, and sell it, then did the Fatimids return it?

The Qarmatians attacked the Sacred House of Allah in the year 317 AH, killing pilgrims, plundering their wealth, desecrating the sanctuary, and taking the Black Stone. They were loyal to the Fatimids and their leader, Ubayd Allah ibn Maymun al-Qaddah (al-Mahdi), who claimed Islam and Fatimid lineage. Al-Mahdi blamed Abu Tahir al-Qarmati for his actions in Mecca and ordered him to return the Black Stone, which he obeyed and returned.