Menu: File > Measurements
The measurements associated with an image Layers are saved as an independent file which has the same filename of the original image plus .MSR file extension.
When the image is reopened, the measurements also will be automatically loaded, and any time the image is saved, they will be recorded as well. If the measurements are cleared, the related file will be deleted when the image is saved.
Saving the measurement with the image in a single file
Although by default measurements are saved as external files, they can also be saved with the image in a single image file, merging measurements with the image..
The layers may be merged by using the Layers menu or by selecting Merge Measurements in the Save As dialog.
After Merge Measurements was selected in the Save As dialog, each time the image is saved again its measurements will be merged and the image flattened. But after the image is closed and opened again, it will revert to the standard way of saving the measurements as an independent file, unless you select Merge Measurements again.
Saving the measurements and the image in another place
Use the File > Save Image as... menu.
Exporting Measurements from the Measurement Pane.