@AnilBhauHindSWa Ok, i'll try to cover this briefly but as clearly as possible:

ब्राह्मण्यं देवि दुष्प्रापं निसर्गाद्ब्राह्मणः शुभे |
क्षत्रियो वैश्यशूद्रौ वा निसर्गादिति मे मतिः ||६||

brAhmaNyam (brAhmaNa-ness) is difficult to obtain; it comes innately; so does kSatriyatvam, etc.

त्रेताग्निमन्त्रविहितो वैश्यो भवति वै यदि ||
स वैश्यः क्षत्रियकुले शुचौ महति जायते ||३३||

After listing all the acts a vaishya should do, including the maintenance of 3 shrauta fires, mahAdeva tells umA that such a vaishya will take birth (jAyate) in a kSatriya family.

गोब्राह्मणहितार्थाय रणे चाभिमुखो हतः |
त्रेताग्निमन्त्रपूतं वा समाविश्य द्विजो भवेत् ||४३||

ज्ञानविज्ञानसम्पन्नः संस्कृतो वेदपारगः |
विप्रो भवति धर्मात्मा क्षत्रियः स्वेन कर्मणा ||४४||

The kSatriya who goes over & above the duties meant for him: who is forward-facing in battle for the welfare of cows & brAhmaNas and he who enters his three shrauta fires [after death]; such a kSatriya becomes a dvija (means brAhmaNa here);

Becomes? In this life? So, a kSatriya can just become a brAhmaNa then? No, because the shloka clearly refers to one who was slain (hataH) for the noble ends and/or reached the other world after being committed to his three holy fires in the cremation (samAvishya). Thus, no doubt.