Will the channel keep its monetization after transfer?

Yes,YouTube monetization stays active on the channel after ownership transfer but if you continue follow YouTube monetizAtion policies, provided you follow the correct process. The channel's AdSense account must be updated to your own AdSense account so that ad revenue is paid to you. If the previous owner had AdSense linked, you will need to change it and link your own AdSense account through YouTube Studio. As long as the channel continues to meet YouTube's monetization policies (no strikes, active content), monetization will remain enabled.