Sorry, that is incorrect.

If Satan is used as an example, the biblical evidence shows that this angel is present with Adam and Eve (Gen 3:1; 2 Cor 11:3) and present in the eschatological future (Rev 12:9; 20:2).

The Bible also states that evil angels are committed to "pits of darkness" until judgment (2 Pet 2:4). What is not clear is what happens to a fallen angel after judgment.

From a human perspective which defines a mortal being as having an end to its life, it appears that angels are immortal.