Is it necessary to rinse the mouth for prayer after eating if ablution is still valid?

Rinsing the mouth after eating is not obligatory; rather, it is recommended if the food was fatty, like drinking milk, because the Messenger of Allah, peace and blessings be upon him, after drinking milk and rinsing his mouth, said: "Indeed, it has fat." That it is recommended and not obligatory is indicated by the fact that Ibn Abbas, may Allah be pleased with both of them, drank milk, then rinsed his mouth, and then said: "If I had not rinsed, I would not have cared." It is desirable to clean the mouth after eating fatty food to remove its traces. The reasoning necessitates the desirability of cleaning even if the food has no fat, although the Prophet's saying, peace and blessings be upon him, indicates that what has no fat does not require cleaning.