Will the channel keep its monetization after transfer?

Yes, monetization carries over through a transfer as long as the channel keeps following YouTube's monetization policies going forward — no strikes, active and compliant content. The one thing that has to change is the linked AdSense account: if the previous owner had their own AdSense connected, you'll need to switch that to your own account through Studio so ad revenue actually pays out to you. As long as that gets done and the channel stays in good standing, monetization itself doesn't reset or pause.