Cemeteries do not always keep obits.
Funeral homes do, however.
One of the many services a funeral home provides is the submission of an obitiary to the newspaper. When you utilize the services of a funeral home, one of the forms they ask you to fill out is an obituary form. The form gives you several blank lines where you actually write out the obituary, or you can allow them to write one for you. They use this form when submitting the obit to the newspaper. This form is kept in their files, along with all the other paperwork.