A man forced his wife to authorize him to throw the pebbles on her behalf although she was capable of doing so by herself?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.

It is impressible to authorize someone to throw the pebbles when a person can do so by himself. A person who commissions another person to throw the pebbles on his behalf whilst able to do so on his own is required to slaughter a sacrificial animal.

As regards the case of a woman whose husband forced her to authorize him to throw the pebbles on her behalf although she was capable of throwing the pebbles herself; if what you refer to as “Forced” is something that inconsiderable under Sharee‘ah, then the woman is required to slaughter a sacrificial animal for not throwing herself. If this forcing is considered (under Sharee‘ah) like if her husband beat her or imprisoned her or treated her in a way that is considered coercion under Sharee‘ah; in such cases she would not liable to anything, as the Prophet, sallallaahu ‘alayhi wa sallam, was reported to have said, “Allaah has forgiven the members of my Ummah for their unintentional errors, forgetfulness and what they were coerced to do.” [Ibn Maajah and Al-Bayhaqi] In this case, it is conditional that her husband directly prevented her from throwing by herself.

Allaah Knows best.