Step 1 Calculate Current Aircraft Empty Moment:
Current Aircraft Empty Weight * Current empty CG
Step 2 Calculate Current prop moment:
Current Prop Weight * Prop Station Measurement
Step 3 Calculate New Prop Moment:
New Prop Weight * Prop Station Measurement
Step 4 Calculate New Aircraft Empty Weight:
Current Aircraft Empty Weight - Current Prop Weight + New Prop Weight
Step 5 Calculate New Aircraft Empty Moment:
Current Aircraft Empty Moment (from step1) - Current Prop Moment (from step 2) + New Prop Moment (from step 3)
Step 6 Calculate New Aircraft Empty CG:
New Aircraft Empty Moment (from step 5) divided by New Aircraft Empty Weight (from step 4)