Yes, you can use the download version of TurboTax self-employed and switch to the online version without having to input all your data again.
This link to the TurboTax Help page How do I switch from TurboTax CD/Download to TurboTax Online? has directions on how to switch from the download to Turbotax Online.
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I think the link above in the first answer is for going the other way from the Desktop program to Online.
If you are asking about continuing your current online return and switching to the Desktop CD/Download program you need this link. And by the way, the Self Employed version is called Home & Business in the Desktop programs.
To continue in the desktop version see this…….
Ok I read your question again. Sounds like you are asking about using the Desktop Home & Business (same as Self Employed version). Then moving to the Online version.
Sorry NO. You can not move a current Desktop return to Online. You can only Transfer a prior year Desktop return into Online. So a 2018 return into 2019 Online. Or next year transfer 2019 Desktop into 2020 Online.