My mom needs home care due to Alzheimer's. How can my sister qualify to be a paid caregiver?

Puerto Rico? Do they have an Area Agency on Aging? That is the best place to find out about available resources here. I imagine Puerto Rico has something similar. Usually, here if a family member is paid it is paid by the elder from their own funds.

http://bexar.tx.networkofcare.org/aging/services/agency.aspx?pid=PuertoRicoAreaAgencyonAgingAAAGovernorsOfficeforElderlyAffairs_687_1_0

Or on this site
https://www.agingcare.com/local/puerto-rico-office-of-the-ombudsman-for-the-elderly-ponce-area-agency-on-aging-pr