Is one way to say Basmalah straight after the first quotation and then recite the second quotation, which is called connecting all together? And what is the other way? Please tell us whether there is a book that discusses this.
After researching and looking into the matter, we did not find any comments of the scholars of tajweed and recitation concerning this particular issue, in the commentaries on al-Shaatibiyyah, al-Jazariyyah, al-Durar al-Lawaami’ and others, namely on the issue of the ways of isti’aadhah (saying “A’oodhu Billaahi min al-Shaytaan al-rajeem (I seek refuge with Allaah from the accursed Shaytaan)) and saying Basmalah when moving from the middle of one soorah to another. Hence we cannot give the questioner the names of the sources and references. But what we found with some contemporary specialists in tajweed is the statement that one may move from the middle of one soorah to another without saying Isti’aadhah or Basmalah; rather one should pause briefly.
Shaykh Husaam al-Keelaani says:
There is no need to say Isti’aadhah or Basmalah when moving from one soorah to some verses in another soorah that are not at the beginning of it. End quote. Al-Bayaan fi Ahkaam Tajweed al-Qur’aan, p. 27.
There may be some evidence for that in khutbat al-haajah which the Prophet (blessings and peace of Allaah be upon him) used to say in his khutbah and which he taught to his Companions. The Prophet (blessings and peace of Allaah be upon him) used to recite in it a number of verses from various soorahs, and it is not narrated that he said Isti’aadhah or Basmalah. It was narrated that ‘Abd-Allaah ibn Mas’ood (may Allaah be pleased with him) said: The Prophet (peace and blessings of Allaah be upon him) taught us Khutbat al-Haajah: Al-hamdu Lillaahi nasta’eenahu wa nastaghfiruhu, wa na’oodhu billaahi min shuroori anfusinaa wa sayi’aati a’maalinaa. Man yahdih Illaahu falaa mudilla lahu wa man yudlil falaa haadiya lahu. Wa ashhadu an laa ilaaha ill-Allaah wa ashhadu anna Muhammadan ‘abduhu wa rasooluhu (Praise be to Allaah, we seek His help and His forgiveness. We seek refuge with Allaah from the evil of our own souls and from our bad deeds. Whomsoever Allaah guides will never be led astray, and whomsoever Allaah leaves astray, no one can guide. I bear witness that there is no god but Allaah, and I bear witness that Muhammad is His slave and Messenger).
“O mankind! Be dutiful to your Lord, Who created you from a single person (Adam), and from him (Adam) He created his wife [Hawwa (Eve)], and from them both He created many men and women; and fear Allaah through Whom you demand (your mutual rights), and (do not cut the relations of) the wombs (kinship). Surely, Allaah is Ever an All‑Watcher over you”
“O you who believe! Fear Allaah as He should be feared, and die not except in a state of Islam (as Muslims) with complete submission to Allaah.)’
[Aal ‘Imraan 3:102]
“O you who believe! Keep your duty to Allaah and fear Him, and speak (always) the truth.
71. He will direct you to do righteous good deeds and will forgive you your sins. And whosoever obeys Allaah and His Messenger (صلى الله عليه وسلم), he has indeed achieved a great achievement (i.e. he will be saved from the Hell‑fire and will be admitted to Paradise)”
Narrated by Abu Dawood, no. 2118; classed as saheeh by Shaykh al-Albaani in Saheeh Abi Dawood.
And Allaah knows best.