In LSP.expert, you don't convert a quote into an invoice. You create a job and then you create a quote and an invoice based on this job.
This is how it works:
You create a job
You create a quote based on this job (Create > A quote) if your client asks for a quote
You define the quote as Accepted or Rejected
If the quote was accepted, you finish the job
Once the job is finished, you invoice it by clicking on Create > An invoice...
... or you select it in your list of jobs and click on the arrow > Invoice selected jobs