In the general case, this wouldn't always be possible because where there is transparency now you'll have opaque pixels after the move, and you can't invent the contents of these pixels(*). However since you state that the pixels are in a white area, we know how to plug the holes... So basically you:
- Get and save a selection on the shape of the hole
- Fill the hole
- Move the selection
- Use the selection to punch a new hole
In slow motion:
- Layer>Transparency>Alpha to selection to get a selection on the holes (and other transparent bits)
- Select>Invert
- Select>Save to channel (this saves the selection for later)
- Re-select the layer in the layers list (because the current "drawable" has become the saved selection)
- Make a rough selection around the letters (Rectangle select or lasso)
- Bucket-fill the selection with white to fill the existing "holes". Do not lose that selection
- Open the Channels list, right-click the saved selection, and Intersect with selection. The selection should become the letters you want to move and only that, the other transparent bits being excluded.
- Start the Move tool, and select the "Move selection" mode in the Tool options (red square icon)
- Drag the letter selection to where you want the new holes to be
- In the Layers list, re-select the layer
- Edit>Clear (or [delete])
(*) Unless the contents is still there and the pixels are just marked transparent. Miracles happen..