Regarding your Question: In accordance with ARA.GEN.360 (d) of Reg. (EU) Nr. 1178/2011, your current authority remains responsible in all licensing and aeromedical matters until such time, that your intended authority has reissued your licence and medical certificate. Therefore, contact your current authority regarding any changes or additions to your licence or medical certificate. “The receiving competent authority shall immediately notify the transferring competent authority once it has reissued the licence and medical certificate to the licence holder and the licence holder has surrendered the licence and medical certificate pursuant to point (c). Until such a notification is received, the transferring competent authority remains responsible for the licence and the medical certificate originally issued to that licence holder.’;”
Until soli is completed and until you get B licence in your hands, your ST for the CPL must be done under A CAA.
Even if you started the process but B CAA didn't process your paper yet, the examiner will see you have a licence A and a medical A therefore the ST report will be under A CAA's rules.