Contrary to what some people on here believe and write - an old dog has very little chance of being adopted.
Kill shelters hold dogs for a few days, if they are not claimed or adopted, they are euthanized - even young dogs don't make it many times, a 12 year old large dog would have almost no chance.
Rescues may take an old dog if they have a place, but again, it is very unusual for anyone to adopt him - I have 2 old dogs that I fostered and kept, for the simple reason that there were no good adoptive homes that applied for them.
It is incredibly cruel to dump a 12 year old dog, whatever your mother's problem with keeping him, please try to help her work out the issues so that your dog can remain with the family he knows for the last few years of his life. Huskies do not live all that long, and he is old already for his breed - please try to get your mother to see that it would be a real cruelty and shame to dump your dog at his age. When she gets old, she will not want to be abandoned by her family, neither does your dog - she really should be teaching you that, but maybe you can teach her.