The Fire Shield spell (PHB, p. 242; emphasis mine) states:
[...] In addition, whenever a creature within 5 feet of you hits you with a melee attack, the shield erupts with flame. The attacker takes 2d8 fire damage from a warm shield, or 2d8 cold damage from a cold shield.
The Imbued Wood Focus (Fernian Ash) (ERLW, p. 277; WGE, p. 114; emphasis mine) states:
[...] When you cast a damage-dealing spell using this item as your spellcasting focus, you gain a +1 bonus to one fire damage roll of the spell.
Does that +1 fire damage applies the first time a Wizard does damage with his Fire Shield?