Changing the habit of login in a system

There's a system that users can either login with their national id and their password OR their customer id and their password. The password is common in both cases for a certain customer (every user may have up to one account since they have one national id).

It is estimated that users can remember their national id better than their customer id, so the preferable way for login in this system is login with national id, and login with customer id appears as a secondary option, recently this system is going to be combined with another system where users are used to login with their customer id (of course they also know their national id, but it's just the way it was before and so they're used to it).

We want to engage the users we already have in the second system to use their national id to login, and yet keep the option of logging in with the customer id open (as it is now in the other system too), the problem is they've never used the national id to login (as it wasn't an option before in the second system), so maybe their preferable way of logging in is customer id till now, and they get confused when they see the field of logging in with customer id is replaced with the field of national id and although they know their national id, they don't see it as a way to login.

But once they know the fact that login with national id and customer id has the same result and their password doesn't need to change, it's estimated that they will prefer national id too. Also the new users to the combined system (no matter which services they want to get) will prefer national id and so customer id will always be a secondary option from now on.

What should be done here to inform the users of the second system that they have a better option to login now and engage them to use this second option?!

Also pay attention that distinguishing between the national id and customer id is almost impossible for the system as long as they may be too similar. So having a field with a placeholder like national id or customer id is impossible here.