This is not possible unless you have the same range of values(min and max) for the renderer to stretch the color scheme across. By definition, a stretched rendering will use the minimum value for the first color, the maximum value for the last color, and pick the intermediate color values based on the stretch between min and max. So, you would need to modify your raster dataset to have the same minimum and maximum values to recreate the same rendering. You could use a con() statement to only keep values within the original range, and then alter 2 pixels at the edge to recreate the min/max you require.
Regards,
Jim