The most straight forward way is, save the image with layers as a Gimp xcf file.
Then to the 'other' image and add the xcf file Open -> Open as Layers
It is possible to drag-n-drop a layer Group from the layers dock to the 'other' open image
Layers not in a Layer Group ? There are plugins and scripts that will move layers into a layer group and also ungroup as required.
One of Saul Goodes scripts attached. Unzip and put in your User scripts folder. Registers in Layers > Stack > Group Linked Layers and Layers > Stack > Ungroup
Works like this: https://i.imgur.com/uQCZgAT.mp4
Link the layers required, into a layer group, drag into the other image (via the tab), ungroup the layers, unlink the layers
Then to the 'other' image and add the xcf file Open -> Open as Layers
It is possible to drag-n-drop a layer Group from the layers dock to the 'other' open image
Layers not in a Layer Group ? There are plugins and scripts that will move layers into a layer group and also ungroup as required.
One of Saul Goodes scripts attached. Unzip and put in your User scripts folder. Registers in Layers > Stack > Group Linked Layers and Layers > Stack > Ungroup
Works like this: https://i.imgur.com/uQCZgAT.mp4
Link the layers required, into a layer group, drag into the other image (via the tab), ungroup the layers, unlink the layers