You typically can't convert the plot shown in the first picture to the plot in the second picture, because the first one is a bitmap.
Depending on the EDX-machine you use, there is usually an option that allows to export the measured EDX spectrum as unprocessed data. For EDX detectors from Oxford instruments it is export as EMSA. Afterwards you can plot it with the program of your choise and it will look like the second image. You just have to assign the elements to the peaks.
There is always a text file with the bitmap image of your spectrum. You can open the text file with exel or whatever and get the graph as you like. to convert the text file into a excel table you have to check the position of the point.