First theory is that the Almoravids conquered Sudan and their wealth started growing. This enabled them to constantly attack Ghana and reduce its power this way and eventually completely dominate and conquer them in a military fashion. This theory is supported by Arabic writings from the 14th century that were discovered.
Second theory is that their religion started spreading among Ghana and their culture and that they got a lot of political power from marrying nobles which enabled them to conquer the area without much war. This theory is supported by lack of archaeological findings of areas with rapid military destruction or areas where wars took place.
