Might be a bit strange for me to ask that question because of my user flair, but I've been going through my books for hours now and can't seem to find the answer.
This is not about when Dönitz knew that Hitler was dead - I know both telegrams by Bormann and the message from Goebbels on May 1st. The question is when he knew that Hitler had died by suicide, because that is not part of the three aforementioned messages from Berlin.
Did he know it was suicide when he spoke to the german public later in the night of May 1st?
Two days gone by and I found the answer myself - I guess nobody will see it, but perhaps someone will someday use the search function.
The answer is: Dönitz didn't know it was suicide. He could've guessed so because Hitler had hinted at committing suicide on April 22nd 1945 when Dönitz was with him, but he simply didn't know.
Source: Mario Frank, Der Tod im Führerbunker. Hitlers letzte Tage