The mustache was probably glued in place and position for the funeral by the mortuary.
Remember when the old wives tale about hair and nails kept growing after we die?
Crazy! It takes live cells to make both. Once the body dies all cells die within hours so it would be physically impossible but there are people who still believe it because those who do believe it; say it with such conviction and no one has ever challenged them on it.
I was talking with a guy one time who said he helped exhume a body once and the nails were “like 3 inches long”. When I explained how he must have been buried that way due to reasons mentioned above; he asked me how many bodies I exhumed like that changes the laws of science somehow. Hey, I gave him an out, I did say he must have been buried that way. People don’t like to be caught in lies. Sometimes they even get violent.
Hair and nails only appear to grow because as the skin and underlying tissue desiccates, it shrinks, so what was once under the skin is now over it.