Liferay supports external user databases (e.g. LDAP) and Single Sign On (SSO) systems. Thus, a good way to support a single log in for many different applications, is to embed an SSO system. Out of the box Liferay supports a lot of them and it's easy to implement support for more.
One way to solve this is to use an external SSO system for your PHP application as well as for Liferay: In future you'd always sign on to that system and PHP as well as Liferay would need to interface with it.
Another way, if your PHP system can't do this is to mimic an SSO system with your PHP application - e.g. have your application forward the user identity to Liferay the way any SSO system would do. Typically this can be through cookies if both servers share a domain. Also, you could do some redirects to known URLs (e.g. encrypt the user's identity in a URL) or have a server-side system that identifies the user and sets some HTTP headers for the following appservers (Liferay/PHP)
How do you do this exactly? Is there anything already available? I fear that this is too complex an answer for this question - especially as I don't know how easy it would be to embed an existing SSO into your PHP application. That's an aspect that is quite important for the choice of strategy.