句子没错。不过你的书写把两个单词连在一起了。应改为：

Just as he reached her，the horse stopped suddenly．

Just as he reached her：时间状语从句。just用在时间连词as前，表示强调。

the horse stopped suddenly：主句。

【翻译】就在他走到她的身边时，马突然停住了。

又如：

He jumped onto the bus just as it was pulling away.  正当公共汽车开动时他跳上了车。

Just as I was busiest, he must come and ask me so many questions.  正当我忙得要命时，他却来问了我好些问题。