Even not taking into consideration complicity it could be argued that Keith is criminally liable for incitement to murder contrary to section 4 of the Offences against a Person Act 1861. Incitement is 'encouraging or pressurising someone to do a crime. But an important aspect is mens rea element. The accused must intend for the person encouraged to commit the crime. The inciter will therefore become an accessory to the offence committed including possible foreseeable consequences that are related to the crime.
In this case he enlists Joe's services to kill his wife, he discusses a fee and an instalment arrangement. The requirement is that it must be 'more than mere suggestion' (Childs, Penny, Criminal Law 2008). This is supported by case law. In R V Fitzmaurice 1983 the monetary aspect was seen as key to the matter of persuasion and 'being more than mere suggestion' (Childs, 2008). The prosecution could argue incitement to murder. Therefore Keith would satisfy both the actus reus and mens rea elements of incitement.
His non payment of the agreed fee would not mean that he would escape liability for incitement or conspiracy as he would have to expressly countermand or 'revoke his encouragement' (Allen, 2007) before the offence is committed or the more than preparatory even in the case of attempts to not be criminally liable for the offence . This is consistent with Becerra (1975) where a 'change of heart' (Childs, 2008) was not considered sufficient, more was required to constitute a withdrawal.
There is also an argument for commission by omission if Keith is criminally liable for incitement to murder it could be argued that his failure to act in a situation he created could constitute an offence. The non payment of the agreed sum would not be sufficient to be considered a withdrawal as previously mentioned but after the agreement it could be argued that there is a duty to act. This however would be difficult and 'it would be for the judge to rule whether the facts were capable of giving rise to a duty' (Allen, 2007).
The third part of the scenario sees Joe stepping up his efforts. His actions of following her out of the gym and pulling out and firing a gun again would be sufficient argument of more than preparatory. Both that and the subsequent pulling out of the knife and stabbing of Jennifer not only satisfies the proximity test in which acts immediately connected with it satisfy that criteria but also satisfy a key principle in R v Whybrow in that the offender intends 'to bring about the any results specified in the full offence' (Childs, 2008).
The actions within the scenario clearly support this. Joe then attempts to dispose of the body but she drowned because unbeknown to him she was still alive. The prosecution could argue that there is a 'coincidence of actus reus and mens rea'. Joe at the time of the initial act had the mens rea for murder but at the time of her death he believes he is disposing of a dead body. Therefore Joe would not have the mens rea element for the 'commission of each act' (Allen, 2008), only the preceding acts.
In the scenario it is clear that death ensued from the final act. The courts however in similar circumstances have been satisfied if 'the accused had mens rea at some stage during the course of events. This is consistent with the 'preconceived plan to kill' (Childs, 2008) Thabo Meli  which mirrors the scenario in that the victim ultimately died not from the blow to the head but from exposure when the assailant had disposed of the body believing him to be dead.
Just like Joe the accused was 'undoubtedly guilty of attempted murder' (Allen, 2008 p 50) but the obiter dicta of the court of appeal in R v Church  approved the 'policy decision' (Allen, 2008 p50) that 'it was sufficient for a conviction if the conduct constituted a series of acts that culminated in her death' (Allen, Textbook, 2008). Using this argument and the approving case law the prosecution could argue that there is sufficient proof of Joe's criminal liability for Murder. Another approach is using factual and legal causation. There is clearly a direct intent to kill.
But as she died as a result of drowning and not the wounds inflicted by Joe it is necessary to prove 'that his act or omissions caused the prohibited consequence' (Allen, 2008 p33). The 'but for' test in R v White establishes factual causation and that 'the consequence would not have occurred as and when it did but for the accused conduct' This was supported by R v Padgett 1983 which also established that the accused conduct needn't be the only cause but it must 'more than minimally contribute to it' (Childs, Criminal Law p7). The death in legal causation 'must be attributable to the culpable act' (Allen, 2008 p34) and in the scenario it is.
There is no intervening act and Joe's act is a major cause in the death of Jennifer. Here again it could be argued that the prosecution would have sufficient proof for a murder conviction. I would surmise that criminal liability for Keith in relation to conspiracy contrary to section 1. 1and incitement to murder contrary to section 4 Offences Again a Person Act 1861 can be established and therefore there is sufficient proof for a conviction. It can also be satisfied that Joe is criminally liable for all of the aforementioned offences.
I believe if murder could not be established however using the coincidence of actus reus and mens rea, or legal causation then there is also sufficient proof for attempted murder. Conversely case law such as R v Church , R v Le Brun , and arguably academics support my conclusion that murder is possible through a 'series of acts' (Allen, 2007) where the mens rea is not present at the culminating actus reus, but is during the course of the preceding linked crime. Using the 'transaction principle for Jennifer and the doctrine of transferred malice for Laura I would argue that there is criminal liability for murder.