About a decade ago, some German university sat and did a study with migrants to Germany and reproduction rates...using Turks, Yugoslavs, etc....going back to the 1950s.
End-result? From those who stayed...first-generation always had the same number of kids as their parents from the old country. Second-generation went to two kids usually. Third-generation went to the German standard of 1.3 per couple.
You can blame birth control....women wanting paying jobs...the cost of living, and the housing situation. But it doesn’t matter. Modern society will only survive if migration occurs in some manner. If you ever introduce birth control to poor regions of the globe, then it’ll trigger a massive global problem.