Tax regulations can be complex and subject to change. It's crucial to consult with a tax professional or accountant who is familiar with both U.S. and Portuguese tax laws to get accurate and up-to-date advice tailored to your specific situation.

However, I can provide some general information that may be relevant to your question:

Non-Habitual Resident (NHR) Status:

The American who has been granted NHR status in Portugal may benefit from certain tax exemptions on foreign-sourced income for a specific period, generally for ten years. This could include exemptions on pension income.
Taxation of Income in the U.S.:

Both individuals will likely need to file U.S. federal tax returns. The United States taxes its citizens on their worldwide income, regardless of where they live. This includes income earned in Portugal, if any.
Taxation of Income in Portugal:

The American with NHR status may have a more favorable tax treatment in Portugal. It's essential to understand the specific rules and benefits associated with NHR status, as they can vary.
Psychologist's Income:

The income earned by the psychologist in the U.S. may be subject to taxation in both the U.S. and Portugal. Tax treaties between the two countries may provide relief from double taxation, but the specifics will depend on the treaty terms.
Denied NHR Status:

The American who was denied NHR status may be subject to regular Portuguese tax rules. They will need to report their worldwide income to the Portuguese tax authorities. Understanding the tax implications and any available deductions is crucial.
Foreign Tax Credits and Exclusions:

The U.S. provides mechanisms such as the Foreign Tax Credit or the Foreign Earned Income Exclusion to reduce or eliminate double taxation. These options should be explored and applied appropriately.
Reporting Requirements:

Both individuals may have additional reporting requirements, such as the Foreign Bank Account Report (FBAR) and Form 8938 for foreign financial assets. These are necessary to comply with U.S. tax laws.