how long it will take is unknown because it depends on whether the other party submits an amended return. if they don't it will take even longer. The IRS after waiting an unknown amount of time to the first notice will send out a second notice asking for proof. they will wait an unknown amount of time to receive responses from both parties. After that the responses will need to be manually evaluated. even if the other party does't respond, the IRS will still review your proof.
the problem is that there is no way to prevent this person for doing the same thing for 2019 unless the IRS bars the person from claiming the dependent.
