Wa alaykum salam wa rahmatuLlahi wa barakatuHu,
In his hashiyah on Ghurar 1/308, Ibn Qasim cited from both Asnawi and Zarkashi, them relating from a nass, that it is recommended for one reciting the Qur’an to also recite the basmaLlah even if starting from somewhere within the surah. The detail of this being in or out of the prayer was not raised in the citation, the nass is general. In Tuhfat al-Muhtaj 2/33, Ibn Hajar’s passage, in which he discusses this point, is similarly general. Even those commentating on Ibn Hajar have observed that these passages imply that there is no difference between one in or outside of the prayer; both may recite the basmaLlah. They point out that the author of Nihayat al-Muhtaj, Shams al-Din al-Ramli, considered this to be the case only for one outside of the prayer. Some commentators on these works indicate to Ramli’s opinion being preferred to them. Insha’Allah, both ways have a basis in the School.
And Allah knows best.
Answered by Shaykh Yaqub Abdurrahman