QB Issue Resolution:

no, QB desktop and QBO are separate programs and they do not talk to each other, you are supposed to use or the other. But if you want to use both, then you have to make duplicate entries in each yourself there is no way to sync one to the other

Resolution for Issue 'Is it possible to sync your Q/b’s on your pc and Q/b’s online? Without having to download the info?' available: Yes (Solved).
Source: Intuit Community forum.

Is it possible to sync your Q/b’s on your pc and Q/b’s online? Without having to download the info?: 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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