I have a different opinion. The verb to murder is rarely used as an intransitive verb and almost always takes a direct object.
The big issue is whether to in "conspiracy to murder" is a preposition or to in to-infinitive. If you replace murder with theft which doesn't have a known usage as a verb, it becomes clearer.
If you Google "conspiracy to theft", you will get 83,700 hits. If you Google "conspiracy for theft", you get only 6,080 results.
Actual usage from IRS.gov:
On July 21, 2015, in Newark, New Jersey, Julio C. Concepcion, of
Passaic, was sentenced to 84 months in prison, three years of
supervised release and ordered to pay $5,643,695 in restitution.
Concepcion previously pleaded guilty to conspiracy to theft of
The linked game site (based in the UK) has some interesting definitions, Law & Order from Catreath.com
Conspiracy to Theft: Planning, aiding or colluding to the taking or
destruction of any item that does not lawfully belong to you without
permission, where the item is worth more than 5 gold pieces, or is
judged to be of particular significance. Theft encompasses the
poaching of game.
It also lists Conspiracy to Assault of a Noble, Conspiracy to Murder, Conspiracy to Murder of a Noble in addition to Conspiracy of Theft. As you can see all the words after the preposition to are nouns.
The reason you don't use the indefinite article a before murder is it is broadly used as a mass noun. You don't usually say one murder, two murders..., but "two counts of murder", "three counts of murder", etc. are broadly used as in:
He pleaded guilty to two (three) counts of murder.
Conspiracy to a noun is more idiomatic than conspiracy for a noun and sometimes the phrase could cause confusion if the preposition to is followed by a noun that could be used both as a noun and a verb such as murder.