I know, the last thing you want to do is to notify the IRS that you moved however it is very important that you do.
Being a former IRS agent and teaching instructor it is critical you receive any documentation that the IRS is sending you.
As an example of this. I have known many taxpayers that have moved and the IRS conducted an audit investigation and made a new tax assessment against them.
Because they did not have current address after the assessments were made the IRS levied and filed tax liens them and the taxpayers had no idea this a taken place.
It is in your best interest to notify them.
 
Question:
Should I notify the IRS of my change of address?
 
Answer:
Yes, if you move, you need to notify the IRS of your new address. We need to change our records so that any tax refunds due to you or any other IRS communications will reach you in a timely manner.
If you filed a joint return, you should provide the same information and signatures for both spouses. If you filed a joint return and you and/or your spouse have since established separate residences, you both should notify the IRS of your new addresses.
There are several ways to notify the IRS of an address change:

• Tax Return: Update your address in the appropriate boxes on your tax return;

• Submit Form: Form 8822 (PDF), Change of Address, and/or Form 8822-B (PDF), Change of Address – Business;

• Written Notification: Mail a signed written statement to an appropriate Service address informing the Service that you wish that the address of record be changed to a new address. Generally, the appropriate Service address is the campus where you filed your last return. In addition to the new address, this notification must contain your full name and old address as well as your social security number, individual taxpayer identification number, or employer identification number;

• Oral Notification: Provide an oral statement in person or directly via telephone to a Service employee who has access to the Service Master File informing the Service employee of the address change. In addition to the new address, you must provide your full name and old address as well as your social security number, individual taxpayer identification number, or employee identification number;

• Electronic Notification: Submit your new address information through one of the secure applications found on the IRS website, such as Where’s My Refund?. In addition to the new address, you must also provide your social security number, individual taxpayer identification number, or employer identification number, as well as any additional information requested by the specific application. You cannot notify the IRS of an address change through other forms of electronic notification, such as electronic mail sent to an IRS email address.

 
 
 
Note:
The IRS may also update your address of record based on any new address you provide to the U.S. Postal Service (USPS) that the USPS retains in its National Change of Address (NCOA) database. However, even if you notify USPS of your new address, you should still notify the IRS directly.
Caution: If you are a representative signing on behalf of the taxpayer, you must attach to the written statement or to Forms 8822/8822-B a copy of your power of attorney. You can use Form 2848 (PDF), Power of Attorney and Declaration of Representative. The IRS will not complete an address change from an “unauthorized” third party.
 
Moving? IRS Requires You to Notify Them and For Good Reasons