Does anybody have an idea how to prove English eligibility in Canadian Immigration?

T-mobile,

if you have your TOEFL score, send that or they have other things too like IELTS, or some stadardized exams that you can take I beleive, it's written on their website.

or else, make a letter from your employer, or your advisor stating that you have proficiency in English language, have them write in their official letterhead, sealed and signed.

hope it helps!

or if you have graduated from US University sent them your transcript, sometimes that will work as well

Most Likely they will ask for IELTS score. you will need to score 7 or more in each section to get full points for English Language.