There was an issue to setup the user in the user picker type field by having only an e-mail of the user.
The plan:
1. pull out user without domain from the e-mail address
2. log through API to JIRA and make a query to find the selected user
3. pick the active selected user in the user picker field
The first point is rather easy stuff.
The second I needed to encode e-mail with api token to base64 and add that into webrequest header:
Add the Headers with Authorization Basic "<EMAIL>:<API_TOKEN>" encoded to base64.
The 3rd point.
Useful links:
How to send web reuqest using JIRA Rest API
How to setup value from text field into user picker field