Changing Workflow assignments
To change who a workflow task is assigned to for any item (e.g. Part or Document etc) in Innovator, you can follow these steps.
Note, this only changes who can complete the workflow task itself (and whose InBasket it appears in), not anything about the related item itself. If (for example when editing a Part or Document) the editing permissions are locked to an individual this will not change. So it's best to only use this technique for checking tasks etc. Other techniques apply to specific cases like claiming the work of editing a Part.
Open the workflow of the item in question:

If there's more than one workflow it'll ask you to choose. Pick the one without a closed date, usually at the bottom...

Click 'Edit' then right-click on the checking task...

Again, click 'Edit' then right click on the assignment you want to change (again, check the 'closed on' column is blank) and click 'replace'.

Choose the name of the new checker, click the 'tick'. Then finally click 'Done' on the 2 workflow windows that you've been editing (note. if you don't click done and leave one of those screens locked then it won't appear in the InBasket - but you can easily retrace your steps above and resolve this).