On 1609 Spain ordered the expulsion of the Moriscos, the descendants of Spanish Muslims who were force-converted to Christianity in 1502. Presumably many of them went to the Muslim lands in North Africa. How were they received there? Since it was more than a century after the 1502 conversion, these Moriscos must not have beem the original converts, but rather their descendants who were born and educated as Christians. According to the Wikipedia articles, there expelled Moriscos numbered about 300,000.
How did the destination countries receive such a large number of people? From their point of view, not only the Moriscos are Christian, they are also foreigners from a country they're at war with. Did those countries welcome them? Were they treated differently from the native citizens, like as something like immigrants or refugees today? Did they convert to Islam and if so how easy/forced was the conversion?
Also, were there any notable historical figures who were part of these émigrés?
The North African "Barbary" states were highly varied. Roughly speaking, the closer they are to their nominal suzerain the Ottomans, the more organized they are. So for example, the state of Tripoli in today's Libya and Tunis were quite sophisticated, whereas Sale in Morocco was a backwater and never quite had the political nor military strength of Tripoli, Tunis, Algiers. Finally, proximity also determined their military investments. Algiers was perhaps the most active and adventurous in terms of piracy, due to proximity to the Spanish coast. Tripoli was less of a threat.
So how were the Moriscos received? The Tunis bey strongly encouraged their immigration into Tunis and considered them Muslims, not Christians. About 80,000 were settled on agricultural lands to the north, and they even participated quite strongly in the trade of Christian captives. There is very little known about whether they practiced Christianity or not, most likely they had lived in segregated communities in Spain in the first place and up to that point still dressed and behaved in Moor fashion.
Some 60,000 of them ended up in Algiers, where the reception was quite a bit cooler. The bey of Algiers suspected that they had become more Christian than Muslim and there was no overt state help in their settlement. Similarly, there is very little material on how they behaved in terms of religion. Notably, rumor of Spanish invasion of Algiers in 1618 led to the edict that Moriscos had to surrender their arms and they had to wear distinctive dress to mark them as Moriscos.
By contrast, Sale's rulers and inhabitants did not welcome the 1,000-ish Morisco immigrants, both due to economic challenges (and thus, they were viewed as competitors) and further suspicion of their loyalty. They were called "Christians of Castile", although there are claims they had integrated as well as they could be expected.
Finally, some segments of Morisco society had been known to engage in banditry and even piracy even when they were still in Spain. These integrated very easily into the Barbary piracy system.
-- E.G. Friedman, North African Piracy on the Coasts of Spain in the 17th Century, The Intl History Review, vol. 1, no. 1, pp 1-16, 1979.
-- A.C. Hess, The Moriscos: An Ottoman Fifth Column in Sixteenth-Century Spain, The American Historical Review, Vol. 74, No. 1 (Oct., 1968), pp. 1-25.