The "Publish" type transition performs the action you are looking for to populate the problems and resolutions tables.  Here is a description on the documentation site: docs.microfocus.com/.../ttst_about_transition_types

When I add a Publish transition, and when I run my existing Publish transition, it only populates the Problem table Title and Problem Description.  I have to create a Solutions table Resolution, and populate the Resolution Description, manually.  Also, the Problem Title and Problem Description are the only fields to which I can map item fields.  So where would the Resolution Description be automatically populated with my Resolution Description?  In a separate Post transition, I assume.

Also, is there a way to have the Problems Table and Resoultions table Submit transitions be Quick transitions?  And would it be possible to simply add a Resolutions Description field to the Problems table so that I only need to submit into the Problems table, to have the Resolution Description displayed?

Unfortunately with the new and improved capabilities in the SRC (Service Request Center) that superseded this old functionality, the mapping to the Resolutions table does not work.  The publish transition should have taken the title and description and pasted to the Problems (which works) then map the system Resolution Summary and Resolution Description fields to the Resolutions table.  The second part does not work.  When we released the SRC interface, it included a knowledge base with superior search capabilities and a workflow that better supports the publishing process.

That being said if you want to use the Problems and Resolutions tables, your best bet is to create an orchestration that creates the Problems and Resolutions table entries and then you can map whatever fields you want from your original record.  Implementing with the orchestration then results in the user experience being just like they were clicking a regular transition where you could present the fields for review that would be mapped to the Problems and Resolutions tables, the user clicks OK and then the records are created.

It is a very simple orchestration that will not take long to implement.  You just need to "CreateAuxItem" web service calls.  If you want to add fields to the Problems or Resolutions tables, they are stored in the Global Process Application.