ESAir title in main phase but no title as assessment stage

I have a client who has Bereavement Allowance at the highest rate (aged 59) who would have title to ESAir at the main phase in SG with EDP; but BA exceeds ESAir at assessment stage; is there any way client can claim ESAir and progress to main phase when there is no title to ESAir at assessment stage.
This has probably been the subject of previous topics but unable to find any so advice or any comments welcome

Yes, claim in usual way, that will establish the period of limited capability for work. Once the assessment’s done complete an ESA3 and irESA will go into payment.

Also, ESA gives NI credits, but I don’t think BA does.