Just taking a quick look at
https://hitachi-id.com/password-manager/features/telephone-password-manager.html it appears that the interface can be digital, analog or VoIP (HMP) on the Hitachi Password server.
Based on the description on the linked Dialogic site, the digital variant needs to be matched to the particular type of PBX (probably emulates a digital station for the connection...we used to work with similar boxes for integration to 3rd party voicemail). Analog would be similar, but probably relying on SMDI (the Dialogic site talks about call info being passed in addition to the call itself...SMDI stuff).
So, your best option would probably to switch it to use HMP and connect via VoIP...but I don't have any specific configuration info to back that up. Sorry!