The open letter to Frieda Schultz (Egon Schultz's mother) is available in German at Chronik-der-Mauer, but no English translation is available. This has been provided below.

In December 1964, near the Checkpoint Charlie border crossing, balloons floated over the wall towards the eastern part of the city. An open letter to Frau Schultz was attached to each of the balloons; it is not known whether or not Frau Schultz, over 230 kilometers away in Rostock, actually received a copy of this letter. This letter was written by the escape helpers who built the Tunnel 57, but the GDR press incorrectly insisted that these escape helpers were the actual murderers, unsuccessfully demanding their extradition. It would not be until after the reunification of Germany that these false accusations were in fact communist propaganda.
Open letter to the mother of Egon Schlultz
Berlin, December 1964

Dear Frau Schultz,

We speak for our group, which, in a half a year built the tunnel through which 57 refugees came, and where your son was shot in front of the entrance.

First of all, we would like to express our sincere condolences for the loss that is so difficult for you.

We have been silent so far about the defamation of communist propaganda, which serve to make border guards and officers more devoted executors of the division of our fatherland.

You should now find out how things really happened on that night of October 5, 1964:

First of all, we want to explain frankly that we four students, who were in the courtyard of the East Berlin house near Strelilzer Straße 55, were armed with small handguns. We had armed ourselves because we felt responsible for the safety of the refugees entrusted to us, and we were also determined, if the tunnel was discovered, to put their lives higher than our own and to allow them to enter the tunnel first. Since August 13, 1961, the border around West Berlin has claimed at least 72 (known) deaths.

On the other hand, we were not willing to be arrested for an act that is allowed in any free country, namely, to bring together people who belong together, and to receive - as has already happened several times - a prison sentence from 15 years to life. But at the same time, we were determined to only fire a warning shot in the event of danger in order to force any border guards to take cover and thus secure our retreat.

At about 12:07 AM, two civilians came to the door, which led into the courtyard, at the end of which was the tunnel entrance in an outhouse. They pretended to be in fear so well that, although they did not know the password, we believed them to be refugees. When asked to take off their shoes to get silently across the courtyard, one of them was about to do so. But the other begged that wanted to get another comrade who had lost his nerve and was waiting nearby. We just wanted to let one of them go, but then the other even started crying out to us. In this dangerous situation, he said, they didn't want to separate. We had no choice but to let the two go. We were aware that if the two of them came back (with a third), three of us would have to handle the refugees. After all, the two civilians had spoken to two of the four escape helpers, who carried their pistols openly.

About 15 minutes later, the two came back with a third man in the middle. The fact that this third person was in uniform was not immediately recognized because of the darkness of the night. "Come with me!" was called in the door to our comrade standing there, who was teamed with the authors of this letter. The uniformed man in the middle gave the command "Load!",and his two companions, who no doubt belonged to the State Security Service, let him go out into the yard.

The distance between our comrade in the gate entrance and the person in uniform was initially only about two meters. Despite the danger, our comrade went backwards, slowly, to hinder the opportunity to shoot a fugitive. The two State Security Service men stayed behind.

Our comrade, threatened by the gun of the uniformed man, had the impression that the uniformed man was surprised by the situation into which he was sent. We can only explain this in such a way that the uniformed man who was brought in had not previously been sufficiently informed of the situation.

One of the three other escape helpers who was in the courtyard immediately recognized the hopeless situation his comrade was in. He fired a warning shot from his pistol to give his comrade the chance to reach the tunnel entrance. The uniformed man immediately opened fire from his submachine gun. The escape helper was in the highest danger of life. And his comrade was cut off from the way back to the entrance to the tunnel. On the run, he shot towards the muzzle flash. A total of 7 shots were fired, by now, from a number of submachine guns, apparently the courtyard was surrounded. About 150 submachine gun shots were fired across the courtyard in one minute. Crouched, the two escape helpers were able to reach the toilet house, the masonry of which withstood the impacts. It was a coincidence that the uniformed man was immediately fatally hit by the few shots fired while running, but none of us by the volleys of submachine guns. The uniformed man may also have been hit by friendly fire, from his own people.

The causal killer is the State Security Service. The men, who had initially played refugees with great acting skills, were unwilling to intervene themselves. They brought in the uniformed men to have the situation rectified.

The actual murderer, however, is the communist government that countered the mass exodus of its own citizens not by eliminating the causes, but by building the WALL and issuing the order for Germans to shoot Germans.

We ask for your understanding that we cannot identify ourselves by name.

Egon Schultz
January 4, 1943 - October 5, 1964
https://www.findagrave.com/memorial/134224590/egon-schultz
Egon Schultz at "Find-A-Grave"