The quick answer to your question is no, the Missionary Sisters do not form part of the Missionaries of the Sacred Heart family.
There are three institutes that do form part of that family, but the Missionary Sisters founded by Mother Cabrini are not one of them. But let me explain.
The Missionaries of the Sacred Heart of Jesus were founded in Issoudun, France, in 1854 by Fr Jules Chevalier. Their initials are MSC, from the Latin Missionarii Sacratissimi Cordis.
The congregation of priests and brothers was founded to promote the knowledge and practice of devotion to the Sacred Heart of Jesus, as made known in the revelations of Our Lord to St Margaret Mary Alacoque between December, 1673 and June, 1675, and to offer personal reparation to the Heart of Jesus.
Their motto in Latin is Ametur ubique terrarum Cor Jesu Sacratissimum, may the Most Sacred Heart of Jesus be loved throughout the world.
The origin of the MSCs is closely associated with the definition of the dogma of the Immaculate Conception of the Blessed Virgin Mary by Pope Pius IX in 1854.
Fr Chevalier found the means to make his foundation through special prayers he offered to Our Lady during the nine days leading up to the definition of the dogma.
On the actual day of the definition, 8 December 1854, he founded the Missionaries of the Sacred Heart.
The institute was officially approved in 1869 by Pope Pius IX, who encouraged the priests in their work in the missions. On 1 September 1881, three MSC priests set out from Barcelona for the South Sea Islands at the request of Pope Leo XIII to begin missionary work in New Britain.
The second institute to become part of the MSC family was the congregation of religious sisters known as the Daughters of Our Lady of the Sacred Heart.
They too were founded by Fr Chevalier, on 30 August 1874 in Issoudun, France. Their first Superior General was Sr Marie Louise Hartzer. From the Latin form of their name, Filiae Dominae Nostrae Sacro Corde, they have the initials FDNSC.
They are often known as the OLSH sisters, and they engage in missionary work and teaching. They first came to Australia from Issoudun in 1885 and now have convents and schools all over the country.
The third institute is the Missionary Sisters of the Most Sacred Heart of Jesus. The institute was founded by Fr Hubert Linckens MSC on 3 August 1899 in Hiltrup, Germany.
It was approved by the local bishop in 1900. Fr Linckens’ deep love for the Sacred Heart, impressed upon him by Fr Chevalier, instilled in him a strong desire to make the Sacred Heart of Jesus known and loved everywhere.
When by 1898 the missionary work of the MSC priests in the South Pacific led to pleas for there to be German sisters to work there, Fr Linckens obtained all the necessary permissions and he founded the Missionary Sisters of the Most Sacred Heart of Jesus.
He was helped in the task of guiding and directing the foundation by Sr Servatia, a Sister of Divine Providence.
Within one year, Sr Servatia, her companion Sr Severine and 26 postulants dedicated themselves to God in the new convent in Hiltrup.
In March, 1901, they took their first profession of temporary vows, and by 1902, a pioneer group of Missionary Sisters of the Most Sacred Heart set sail for the South Pacific.
By 1904, 10 more Sisters had arrived. The sisters came to work in Australia in 1928 from the United States.
So, while the Missionary Sisters of the Sacred Heart of Jesus founded by Mother Cabrini and the Missionary Sisters of the Most Sacred Heart of Jesus founded by Fr Linckens have essentially the same name, and both have the initials MSC, only the second institute is part of the MSC family founded by Fr Chevalier.
We can pray for the fruitfulness of the work of all these institutes throughout the world.