Because the passive memory comes from antibodies instead of B cells themselves, infants do not inherit long-term immunological memory from the mother.

How immunological memory is generated?

Immunological memory occurs after a primary immune response against the antigen. Immunological memory is thus created by each individual, after a previous initial exposure, to a potentially dangerous agent. The course of secondary immune response is similar to primary immune response.

Can you inherit immunity from parents?

One way in which intergenerational protection can manifest is by parents directly providing active immune components such as antibodies to their offspring. In mammals, including humans, mothers transfer antibodies through the placenta or in their breast milk to help protect their offspring from disease early in life.