Can witnessing injuries resulting from a husband's beating be considered testimony to save the wife, who repeatedly returns to her family because of this, while the husband refuses to divorce her?

Testimony is not permissible unless based on knowledge and certainty. Therefore, verification is essential in testimony, as Allah Almighty says: ﴿إِلَّا مَنْ شَهِدَ بِالْحَقِّ وَهُمْ يَعْلَمُونَ﴾ [But only those who testify to the truth, and they know] and His saying: ﴿وَالَّذِينَ لَا يَشْهَدُونَ الزُّورَ﴾ [And those who do not bear false witness]. If a person testifies about an action such as beating or causing damage, knowledge of such an action can only be attained through sight and direct observation. Hearing or seeing the traces of wounds is not sufficient.