You should apply for adoption leave from your department in writing, notifying them of the dates you expect to leave and return to work. Your department will then notify Financial Services that you are going on leave.
Adopting parents are entitled to 37 weeks of unpaid adoption leave, and you must complete your adoption leave within the first 52 weeks of your child arriving in your home.
To coincide with EI weeks and avoid any possible loss of EI benefits:
You should apply for Employment Insurance (EI) Parental Benefits from Human Resources and Skills Development Canada as soon as you receive your Record of Employment (ROE) from Financial Services. (Ensure that Financial Services has your current home address since they will mail the ROE after your last paycheque has been generated.)
Your ROE can also be picked up in person, either by making an appointment with your Financial Services Representative, or by proxy if they have a signed letter authorizing them to do so.
Details on applying for Employment Insurance Parental Benefits can be found at Service Canada.