Hi Jo Ellen,
We have this happen quite frequently here in Maine and at all three of my cemeteries, we do list them both in our paper records as well as our online records. We do, however, specify that is is a cenotaph and will reference where the body is actually interred.
As an example, a child was buried at the only Jewish cemetery in Maine. When the new cemetery was founded in 1894, the family purchased a family plot in the new cemetery and placed a memorial marker for the child buried at the other cemetery.
We list it as a courtesy and sign of respect for the family, as well as to help with the confusion of multiple online records.
Hope this helps!
Sherri