Even if you shared your list in Wunderlist you are still not able to share to-dos of this particular list with anybody else?
One reason for this might be that the person you shared the list with does not have a Wunderlist account yet. As soon as you complete the sharing process the person affected will receive a Wunderlist invite send to the email address you used. Now, he/she has to set up his/her own account in order to be able to see the shared list.
The person affected already has a Wunderlist account or just set up an account and it is still not working?
Please recheck if you used the correct email address. Wunderlist for Outlook allows you to sync other accounts to your Outlook which means that the email address needed might not be an Outlook address but a private one.
Upon sharing, the relevant person will be notified of this operation. However, he/she will have to accept the sharing invitation in his/her Wunderlist account first. Only then you are enabled to assign tasks to them. You will see if the person accepted your invitation by the new “Assign to” feature in the Wunderlist sidebar.