load your vertex colored YourFile.PLY to Meshlab;
Run Filters/Texture/TrivialPerTriangleParametrization and apply
Run Filters/Texture/VertexColorToTexture (ML saves the texture png to the folder where your PLY is located named as YourFile_color.png)
Export (maybe to obj) to the same folder. Although the export dialog does not show the texture (make sure that TexCoord is enabled – should be now by default) the obj comes with a linked .mtl file.
Edit the mtl file in a texteditor and simply add this line:
(replace „YourFile_color“ with the name of the created texture and save the modified mtl – this links the png to the obj)