Answer by Danavir Goswami
The Lord also declared to Yogamäyä, “My plenary expansion Ananta Çeña is within the womb of Devaké. On account of being forcibly attracted to the womb of Rohiëé, He will be known as Saìkarñaëa and will be the source of all spiritual power, or bala, by which one can attain the highest bliss of life, which is called ramaëa. Therefore the plenary portion Ananta will be known after His appearance either as Saìkarñaëa or as Balaräma.” (Krishna Book)
This is corroborated in the Gopala Campu of Jiva Goswami, First Campu, Tritiyam Puranam as follows:
94. “Her heart withered by cruel Kamsa’s ferocious words, Rohini complained to Vasudeva, and Vasudeva sent her to Vraja. Riding on a horse, Rohini secretly entered the land of Vraja at dusk. Seeing chaste Rohini’s arrival as an auspicious omen, everyone in King Nanda’s assembly became happy at heart. Overcome with joy, Rohini and Yasoda embraced. They were like the Ganga and Yamuna flowing together.
95. “Then it was the month of Jyaistha. Seeing that Rohini was three months pregnant, Yasoda became very happy.
103. “Then Goddess Yogamaya suddenly ended Rohini’s seven-month- old pregnancy and placed in Rohini’s womb an unborn child taken from Devaki’s womb. Then, in the fourteenth month, the month of Sravana, when the auspicious star Sravana conjoined with the moon, joyful Rohini gave birth to a handsome son glorious with all transcendental qualities. She was like a glorious moon effulgent with moonlight. She was like a lioness who has given birth to a very powerful cub. She was like a fresh lotus-lake in which a fragrant white lotus flower has bloomed. She was like pure knowledge that has given birth to all-auspicious glory.
104. “Rohini gave birth to a son with a glorious face, lighting-flash eyes, dark-cloud hair, a white autumn-cloud form, and great glory and prowess. Her son was very glorious and transcendental.
105. “Her son’s form was fair and powerful without limit. The astrologers said, ‘This boy will be the elder brother of the Supreme Personality of Godhead. He will be the protector of the cows, and the killer of Dhenukasura, Pralambasura, Dvivida, and a host of demons. His arms will be long, His name will be Rama. In a past life He enjoyed pastimes with Lord Ramacandra.’
106. “Sent by Vasudeva, learned brahmanas named Sarma performed the nama-karana and other ceremonies for Balarama.
So as far as Bhagavatam and Gopala Campu and the comments of Srila Prabhupada are concerned, Balarama was transferred from Devaki’s womb to Rohini’s womb after seven months of Rohini’s pregnancy. She became impregnated by Vasudeva in Mathura before she went to Vrndavana.