If they are requesting you to fill out Schedule A, then they require travel history from the principal applicant, not the sponsor.
- Schedule A Background / Declaration: https://www.canada.ca/content/dam/ircc/migration/ircc/english/pdf/kits/forms/imm5669e.pdf
Please ensure that you do not leave any time periods unaccounted for. Pay particular attention to questions 08-12 of the Schedule-A form and provide all details since the age of 18 years. Please do not leave any question unanswered/blank. If any question is not applicable to you, quote “Not Applicable”.
- IMM5406 Additional Family Information Form: https://www.canada.ca/content/dam/ircc/migration/ircc/english/pdf/kits/forms/imm5406e.pdf
- IMM 5562: Supplementary Information - Your Travels form: https://www.canada.ca/content/dam/ircc/migration/ircc/english/pdf/kits/forms/imm5562e.pdf
These are the forms they are requesting. I am asking about the 3rd one 'Your travel history',