Baha’u’llah in his testament appointed Muhammad-‘Ali to succeed ‘Abdu’l-Baha.

Immediately after the death of ‘Abdu’l-Baha, his half-brother Mirza Muhammad-‘Ali had advanced the claim that he was ‘Abdu’l-Baha’s rightful successor. He announced this claim not only directly among the Baha’i communities, but made use of several Egyptian newspapers. In the United States, Shua‘u’llah functioned as a propagandist for Muhammad-‘ Ali. Muhammad-‘Ali and his followers evidently tried to make use of the mass media in pursuit of their goals in other countries, too. His claim was based on the succession regulation set out in the Kitab-i-‘Ahd, the testament of Baha’u’llah. In this document, Muhammad-‘Ali had been appointed successor to ‘Abdu’l-Baha. However, since Baha’u’llah had explicitly made this appointment dependent upon Mirza Muhammad-‘Ali’s continued loyalty to the Covenant, and Muhammad-‘Ali had refused to follow ‘Abdu’l-Baha, had opposed him and become a covenant-breaker, the Baha’i communities did not recognize his claim. The campaigns conducted by Mirza Muhammad-‘Ali caused something of a stir but had no significant effect. Muhammad-‘Ali did not win any support in the community and his few followers eventually reintegrated themselves into the Muslim community.

(Making the Crooked Straight: A Contribution to Bahá'í Apologetics, by Udo Schaefer, p. 714)