QB Issue Resolution:
Your Purchase transactions should be where you use Items, and you Track that this is for that customer as billable to them. Right now, you are running income and expense through the same account = Net is 0.
Open Help and search on Work With Items; yours should be Two Sided. I will attach images for your reference and one Handout that explains a lot of this.
Resolution for Issue 'Revenue not reporting correctly. Bills that are entered and invoiced direct without any markup show as reimbursement and show as $0 in revenue' available: Yes (Solved).
Source: Intuit Community forum.
Revenue not reporting correctly. Bills that are entered and invoiced direct without any markup show as reimbursement and show as $0 in revenue: 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 attach images
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