Can "his murder" mean two different things?
- The murder of a male person (him)
- A man's crime, e.g His murder of someone
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Just to add to the answers you already got, here are a few real examples linked by this ngram.
Being the victim
"Now the hour had come, and an unstoppable chain of events had begun that would end in His murder." (The murder of Jesus)
"It was only after his murder that I gradually learned about the circumstances surrounding his death." (Human Rights in Northern Ireland)
Being the murderer
"The defection of Bogdan Stashinsky in 1961 was prompted not by his revulsion of his murder of the Ukrainian politician, whom he killed with an ingenious cyanide gas gun in October 1959, but [...]" (The A to Z of Sexspionage)
"The murderer is presented as having committed his murder in the necessary pursuit of his duty." (Psychoanalysis, Literature and War: Papers 1972-1995)
I would like to credit DamkerngT for the idea of using the verb "commit" to provide enough context to interpret "his murder" as "his murder of a victim".
Context, context, context!
Simply leaving his murder will be something like aiming in the dark! But still, let me try.
What are you talking about? He confessed, really? "Yes, he did. He confessed for his murder and is now repenting his awful act." - here, he murdered someone.
If it was in the context of a trial, the phrase could be used that way...
Oscar Pistorius was the target of relentless and combative questioning Wednesday as the prosecutor in his murder trial tried to... - here it means he murdered someone and its trial going on.
On the other hand,
That desire ended in his murder, following an attack that was without mercy - his murder was barbaric. - here, he was murdered