QB Issue Resolution:

you can not

they are separate software packages and do not communicate, intuits concept is that you use one or the other but not both

If you need internet access to desktop look for a hosting service for desktop or check out Qbox and myquickcloud

Resolution for Issue 'I have a quickbooks online account that I have been using and I also want to use the 2015 quickbooks contractor addition at home on my pc. how do I connect the two.' available: Yes (Solved).
Source: Intuit Community forum.

I have a quickbooks online account that I have been using and I also want to use the 2015 quickbooks contractor addition at home on my pc. how do I connect the two.: 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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