QB Issue Resolution:

in QBO you have to use a journal entry AFTER you make the adjustment to shrinkage

report on the shrinkage account to find the cost that was posted as a result of the adjustment, then create a journal entry

debit expense $$
credit inventory shrinkage $$

Resolution for Issue 'How do I write off inventory to an expense account other than “inventory shrinkage”?' available: Yes (Solved).
Source: Intuit Community forum.

How do I write off inventory to an expense account other than “inventory shrinkage”?: 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.

Support for Expense Account
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Error Recovery for Expense Account [Canada]
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