A wall adapter system (10) having a wall adapter (12) is disclosed. The wall adapter (12) permits a mullion (16) to be secured to a wall (14) through the wall adapter (12) without the need for trimming or caulking. The wall adapter (12) has a front portion (26) with a mullion snap interlock (56) and first and second side portions (28, 30) with snap cover trim interlocks (68). The mullion (16) is snap fit on the front portion at the interlock (56) while cover trim (70) are snap fit on the side portions (28, 30) at the snap cover trim interlocks (68). The front portion (26) can be formed into parts, a main portion (104) and an adjustment portion (106) which allows the wall adapter to be mounted to a range of wall thicknesses. The wall adapter (12) can be used with a block header (150).