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Well your first job is obviously to shoot the manager, for
a) hiring the wrong person
then
b) making the team's performance dependent on him/her
No team should be dependent on one person, so that must be fixed as a matter of urgency. (What happens if the guy leaves tomorrow?)
An unstable personality can't be fixed, but it can be helped and the effects mitigated. The person is clearly an asset to the business and so a way should be found to keep them if at all possible. However, unstable personality can be devastating to a team (and the whole business, if it is small) and in the last resort it may be necessary to invite the person to leave.
Speak to the person and understand his problem make him feel comfortable with all kind of support that your next to him always treat him as good friend and you are there to resolve his issues and problems.
Guidiing him to be stable personality in the way I demand.