Based on the fact this is is a .com domain, you can do the following:
Go to https://www.verisigninc.com/en_US/domain-names/com-domain-names/index.xhtml.
Click on the Chat with Support link at the bottom of the page. Explain the situation to them and tell them what documentation, if any, you have to establish that you or your client is the rightful owner of the domain. They will let you know if they can make the transfer or will need some kind of legal order. It may be that they will direct you to the registrar through which the .com domain is registered, in which case you may need to contact their support and if they are not helpful then escalate the issue to network solutins / Verisign.
Ideally, your order of laying claim to the domain should be:
- With the registrar,
- If they don't help, with Verisign,
- If they don't help, time to get a simple court order advising both the old web developer and the registrar to comply with the court's order. It rarely ever comes down to this, unless your client owes the web developer some money, in which case this is more than a domain issue.
What is the domain extension. Is it a .com, .co.uk or something else? Different companies are in charge of different TLDs. For instance, to deal with .com domain issues you will ultimately need to contact Network Solutions. To deal with .co.uk issues, you will need to contact Nominet. I have had a similar issue with a .co.uk domain name before, so have some experience with it.
Having a legal name similar to the domain will help, but it is pointless if the business is registered after the domain name - it doesn't give you any precedence.
What you need to do is have this kind of paperwork to say this IS your business, but then also provide the registration authority who runs the domain TLD with other documentation / communication showing that the domain was registered by an agency or web developer for your business. It is up to them to decide - they may think some company registration documents with some email communication with the developer is enough.
Nominet in the UK is actually really quite helpful like this. I can provide more information if you let me know the domain TLD.
Another option is to get a solicitor / lawyer involved who sends a legal warning to the last developer. Your client can send this directly too. This too will help establish that you are trying to solve the dispute amicably - everyone will ask you for evidence that suggests you have done this before taking any action.
Eventually, you need to put together a paper trail showing the last guy is misbehaving and provide it to the registrar or registration authority. If they do not co-operate, go to court and get a legal order advising them to change the details.