transferring values into other features

Dear all,

with the tool "Split" I cutted the forest areas of a province into square fields. Please see the attached screenshot for illustration.

The resulting forest layers have an attribute with the geometry values of the single polygons. In the attribute table I can read the sum of the area values in the square fields. But now I want to add this value sum (of how much forest area there is in one square field) as an attribute value to the square polygons. Is there an elegant way to proceed this?

Thanks in advance and kind regards,
Matthias

Attached Thumbnails