ASPxGridView - How to correct the column layout if column widths are set in percentages and the grid is grouped

This example illustrates the solution for the first issue described at ASPxGridView - Why column layout may become broken after user actions if certain column widths are set in percentages. 
The main idea is to determine the widest column and delete its setting. As a result, the widest column will fill the space that appears after moving one of the columns to the Group panel. 
For this, we implemented the GridViewColumnHelper class and use ASPxHiddenField to preserve information about column width between requests to the server.