TL;DR
The loss or malfeasance of key personnel is always a project risk. You can often mitigate such risks through technical or administrative controls, separation of duties, and cross-training, but the risk level will never be zero.
Once a risk is actualized, preventative controls are rarely practical. Instead, you will need to trigger (or create) detective, compensating, or administrative controls to handle the current situation, and then inspect-and-adapt your process to control for similar risks in the future.
Acknowledge and Address Project Risk
Is there anything I can do to get him to do his job and provide the handover?
You can't make someone do anything. Even if you are in a position of authority (project managers often lack direct authority), you must still rely on your business processes and interpersonal influence to get the results you need. If the company has already burned its political capital with this employee (or vice versa), and you can't rely on either the employee's professionalism or on existing business continuity processes, then you probably need to accept the situation for what it is, and then move on to system recovery or exploratory testing to address the project risk.
However, apart from releasing him early, it seems we've no other recourse.
You might get other answers over at The Workplace, but from a project management perspective it is often too late to avoid or mitigate this type of business risk post-facto. In the future, you should:
- Ensure your project team is cross-functional. Everyone on the team should have at least basic knowledge of how the system works, where key elements are documented or stored, and have a role in business continuity planning.
- Guard against low bus factors in your project. No individual should ever be the single point of failure for your system or your process!
- Have a documented business continuity plan (BCP) that includes knowledge/password/key escrow and clearly-defined recovery processes.
- Proactively test business continuity and disaster recovery plans. Don't wait until someone quits or is fired to discover whether your plans work effectively!
- Have a clearly defined process for onboarding and offboarding people from the project, including the granting and revocation of access to your project resources.
In short, if you have no influence with this person, and no meaningful incentives to offer that might encourage constructive collaboration during this transition period, then the business should cut its losses, accept that foreseeable personnel risk has come to pass, and begin implementing sensible next steps (whatever that means for the current project and the organization).
You can't close the barn door after the horse has bolted. This risk can no longer be avoided, so focus on what the project needs to move forward rather than on spinning your wheels about how the project got to this point. Just make sure the organization learns the right lessons from this experience, and doesn't end up here again in the future.