QB Issue Resolution:

The Sync with Square integration does not automatically copy over your inventory list from Square into QB Online.

However, you can setup your QB Online with an identical item list by exporting your list as a csv from Square and importing it into QB Online yourself. Then, the Sync with Square integration will record sales and decrement item counts accordingly in QB so long as the item name and/or SKU in QBO matches what your have in Square.

Resolution for Issue 'If I get QB Online and sync with Square, will Square send QB inventory data?' available: Yes (Solved).
Source: Intuit Community forum.

If I get QB Online and sync with Square, will Square send QB inventory data?: 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 QB inventory data
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Error Recovery for QB inventory data [Canada]
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