The only reference similar to what you ask would have been in Operation Corona , when some British planes carried German speaking radio operators to give wrong directions to nightfighters.
That said, I doubt this would have been tried beyond tactical, immediate level in air combat, because: The setup was not easy (including finding radio operators who spoke the enemy language well enough to confuse the enemy).
Land troops would intensively used campaign phones, and the operators would be probably able to recognize who they were talking to (between communications would usually be from HQ to subordinate units).
Non-urgent messages would have been coded, or even delivered personally.
Even if you had the enemy codes, letting the enemy know that you have the codes for a small tactical advantage is just the thing you should not do.
The situation would be less fluid.
Even if you gave an unit an order to abandon the positions, that order would take some time to comply; during that time the ruse could be discovered.
If you gave the enemy time to discover the ruse, things could be wrong.
One thing with deception is that you are giving away your intentions (tell the enemy to remove their forces from one position and, if the enemy discovers you, now the enemy knows which is your objective).
history.stackexchange.com/users/8820/SJuan76
During WW2 the British used an actor who bore a striking resemblance to Montgomery , to throw off the Germans as to British intentions on invading France.
M. E. Clifton
James was noticed when he appeared as 'Monty' in a British stage production, and was recruited by fellow actor David Niven to actually impersonate Montgomery, to the edification of German intelligence sources.
The goal of Operation Copperhead was to hint to the Germans that Monty was actually interested in southern France in early 1944.
The effort appears to have been at least partially successful.
history.stackexchange.com/users/25614/tj1000
A classic example would be the pre-D-day deception aimed at making the German's believe that the actual invasion was to take place at the Pas de Calais.
An entire fake army, the First United States Army Group was invented as part of Operation Fortitude South .
To help sell the effect and convince the Germans that this was the main invasion force, a large deception operation created fake equipment, such as camps, dummy landing craft and airstrips, to look like a real army was being prepared.
This was supplemented with wireless traffic between these fake units to simulate real operational communications.
In addition notable senior staff, such as General Patton, were (supposedly) attached to the army to give it some credence.
history.stackexchange.com/users/6489/Steve Bird
When the Americans landed at Salerno, loudspeakers blared out in the best Hollywood style, "Come out with you
're hands up.
We've got you covered."
Not spies, exactly, but certainly "voices."
The Americans refused to surrender, and won the battle.
history.stackexchange.com/users/120/Tom Au
Most (in)famous (and most controversial) use of voice actor was Norman Shelley's impersonation of Winston Churchill in some of his most important and most famous speeches.
Allegedly, Churchill had very unpleasant high-pitched voice, and he could not be bothered to record his speeches.
Therefore, voice actor took his role and recorded 'We shall fight them on the beaches', 'Their finest hour' etc .
Later, in 1949.
Churchill re-recorded those speeches with use of new equipment.
This topic is still hotly contested, with various claims and counter-claims, but as you could see from links below, there is physical evidence(records) that Norman Shelley indeed did record some of Churchill's more famous speeches.
Finest hour for actor who was Churchill's radio voice Norman Shelley Churchill's voice - 1909
history.stackexchange.com/users/25411/rs.29
I am mostly referring to WW2 and cold war when embedded spies could have impersonated officials on low levels to carry out orders which were never issued.
Have voice actors ever been used to impersonate military or political officials to trick the enemy into doing something?
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<espionage>
history.stackexchange.com/questions/38860
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Norman Shelley is said to have impersonated Churchill in some of his most important speeches. The British also carried German radios to give the wrong orders to nightfighters.  It is widely believed that actor Normal Shelley was the true voice of some of the Winston Churchill's war-time speeches. However, whether this was done to deliberately mislead the enemy is another matter. Additionally, during the second world war, British planes may have carried German-speaking radio operators to try to deceive German fighters. It is also claimed that an actor played the role of General Montgomery in an attempt to mislead German forces about British movements in France.
It is believed that some British planes carried German speaking radio operators during the Second World War to mislead German fighters. Durring the Second World War, the British used an actor to play a general in order to mislead the Germans about British manoeuvres in France. It is widely believed that actor Norman Shelley was the true voice of some of Winston Churchill's speeches.