Dear Sir,
This looks doable with us.
We require both source (shared server) and destination (Godaddy Business server) details, we will manage to get you nice, smooth and quick switching.
For now, we have estimated 10 hrs at USD8/hour of rate for this task. In case, if we will require more hours for the reasons like sizable website which require lots of download and upload and settings up things there, like crone files etc.
Please share more details, so we can guide you closely.
We can start this work on an immediate basis.
Let's do it nicely for you.
Best regards,
- Prakash
WeTheDevelopers