QB Issue Resolution:

First run QuickBooks->Check for Updates and make sure you have the most recent version of 2019. Then find your 2016 files (in the Finder click on Spotlight and search for .qb2016 to see all the 2016 files you have).  Inside of QuickBooks Mac 2019 choose File->Open and navigate to the 2016 files. It should be able to open them.

Resolution for Issue 'is qb 2016 compatible with mojave? just upgraded to qb 2019 and no files after 2014. qb support said its not compatible with mojave and wants $399 to fix corrupted files.' available: Yes (Solved).
Source: Intuit Community forum.

is qb 2016 compatible with mojave? just upgraded to qb 2019 and no files after 2014. qb support said its not compatible with mojave and wants $399 to fix corrupted files.: this issue or error code is a known issue in Quickbooks Online (QBO) and/or Quickbooks. Support for this issue is available either by self-service or paid support options. Experts are available to resolve your Quickbooks issue to ensure minimal downtime and continue running your business. First try to resolve the issue yourself by looking for a resolution described below. If it is a complex issue or you are unable to solve the issue, you may contact us by clicking here or by using other support options.

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