I am not familiar with Amember4, but just did a general look at it to understand context.
I think that what is happening here is that Moodle internals have changed quite a bit from version 1.9 to 3.0. What I am thinking is, maybe Amember4 uses Moodle's web services, and maybe some of those web services have change enough to break the integration. You may want to find out if there is an updated version of the Moodle integration plugin. It is not clear to me if there is an amember4 plugin that gets installed to Moodle or not... Or if amember4 has a plugin that gets installed. I didn't find any reference to amember in the Moodle plugins database.
....5 minutes later...
Did a little more searching and found: https://www.amember.com/p/Integration/Moodle/ The readme.txt in the download file posted there only references Moodle versions 1.7 and 1.8. It also appeared that there is a Moodle side plugin for this integration. I think what I said is true, that this plugin probably is not going to work without some re-factoring to support Moodle 3. Maybe someone has done that already, but I wasn't able to find it.
Sorry I am not more helpful.