This cannot be done with the usual Copy / Paste, because there is no such option to paste with offset results.
This can be done, for example, with formulas, provided that the glued areas are of the same size.
Since you did not include your files, in my example you have to adjust the example. The idea behind the formula is this:
where
lks stands for the number of merged cells.
You copy this formula down until your data is exhausted.