Some landlords may not know how to write the letter even if he or she agrees your mum stay with you. To make things easier, you can draft the letter for them and they just need to sign it provided they are happy with the letter.

Below is the sample letter for the proof of accommodation for visa purpose.

To whom it may concern:

This letter is to confirm that (Your name) has been living in (address of the property) since (starting date of your tenancy).

I acknowledge that (your name)'s mother (your mum's full name) will be visiting (your name) during the period of ( specific time frame ), and I agree both of them stay at (property address) during that period.

if you have any concern please feel free to contact me at (landlords phone number).

Regards

Landlord's Signature
Date

Hope it helps. You can also find some other samples here.