QB Issue Resolution:

You can not mark the lines that are paid, in QB the whole invoice is considered one amount, and you receive full or partial payments on that.

In reporting though it changes, if you are accrual based then the sale income is posted when you save the invoice

in cash based reporting, QB will allocate a portion of the partial payment per item line on the invoice and for sales tax, you have no options as to how QB does the allocation and it only shows up on cash based reports

Resolution for Issue 'How can I enter a partial payment on an invoice but mark the lines that were paid so i know what is still open on that invoice? entering partial payments but checking off the items that were paid so I would know what items are still open in that invoice' available: Yes (Solved).
Source: Intuit Community forum.

How can I enter a partial payment on an invoice but mark the lines that were paid so i know what is still open on that invoice? entering partial payments but checking off the items that were paid so I would know what items are still open in that invoice: 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 enter a partial payment on an invoice
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Error Recovery for enter a partial payment on an invoice [Canada]
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