B cells are indispensable for priming the defense against infection with heterosubtypic influenza virus strains. In cooperation with memory T cells, naïve B cells reduce morbidity and promote recovery upon heterosubtypic infection:

Article Host Immune Response to Influenza A Virus Infection

Also, kindly check:

Memory killer T cells are primed in the spleen during influenza infection:

https://www.uab.edu/news/research/item/12268-memory-killer-t-cells-are-primed-in-the-spleen-during-influenza-infection

There are real vaccines against influenza viruses, however the virus mutates quickly. In fact, there are 2 mechanisms of mutation: antigenic drift (gradual accumulation of mutations of HA or NA antigenes) and antigenic shift (sudden drastic change in antigen, usually HA)

Antigenic drifts could be "targeted" with vaccines aimed against influenza-viruses present the past year (selected in february by WHO). But since there is mutations, the vaccine is not 100% efficient and needs to be updated yearly.

On the other hand, antigenic shift is not predictable and can lead to epidemic or pandemic.

Source:

https://en.wikipedia.org/wiki/Influenza#Antigenic_drift_and_shift

If you are more interested, there are researches to elaborate a more powerful vaccine:

- Sautto GA, Kirchenbaum GA, Ross TM. Towards a universal influenza vaccine: different approaches for one goal. Virol J. 2018;15(1):17. Published 2018 Jan 19. doi:10.1186/s12985-017-0918-y

- Kim YH, Hong KJ, Kim H, Nam JH. Influenza vaccines: Past, present, and future. Rev Med Virol. 2022;32(1):e2243. doi:10.1002/rmv.2243