Change your default calendar to your desired account:
- Go to device Settings
- Go to Calendar (or Mail, Contacts, Calendars in iOS9 and below)
- At the bottom select Default Calendar and pick the iCloud account of your choosing.
This ensures all future events added through Siri or other calendar apps that sync with your phone will automatically be added to this account.
In Week Calendar Settings (gear button) > Calendars select only the local calendar you want to convert
If you've more than one convert them one by one unless you want them to be merged into a single calendar.
- Press Settings > Share & Print
- Select Export
- Select Date Range to Export (this is limited by iOS to 1 year max)
- Select Type and mark ICS File
- Press Export
- Select Send by E-mail and mail file to an e-mail account available on your PC or Mac so you'll have a backup
Open the email you just sent and click on ics file. You'll get a question in which calendar you would like to import these events.
After you verified all events are synchronized correctly you now may want to delete your local calendar.
See https://weekcalendar.zendesk.com/entries/28941432 for instructions.