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主申请人去中国出差，最近两个星期有关键的业务，不能回来。他妻子和女儿想就近去墨西哥然后回来。
-That will a big problem for the wife and the child to stay in US due to their current I-94 will expire very soon. They have to go back to China before the I-94 expires. Then, come back together with the L-1A beneficiary (the husband).

所以：

1、从墨西哥回来的时候，只有妻子带着女儿入境，而I-797B上批准L1A只有主申请人的名字，她们能入境吗？
-No. They can not use that I-797B to enter US if they leave US because that I-797B is not activated (the L-1A holder has to use it to reenter US first, then the dependents can use it to get the L-2 status). By the way, if the husband extends his L-1A status within US in the future (e.g. next year), the wife and the child have to file the L-2 status extension at the same time. So, it seems the lawyer is very poor/inexperienced.

2、去墨西哥的时候，只有妻子带着女儿，主申请人没有同行，需要主申请人（孩子的父亲）的授权书吗？
-They can not go to Mexico, otherwise they can not reenter US because the I-797B is not activated.

Another choice is that the husband come back to US using the L-1A approval notice (I-797B)) before the wife and the child L-2 I-94 expires, then the wife and the child can file L-2 extension within US.