如果你能立即把这本书寄给我，我将不胜感激。

I would be most grateful if you would send me the book immediately.

如果你能给我任何建议，我将不胜感激。

Any advice that you can give me would be greatly appreciated.

如能……我们将不胜感激。

Eg. We world be very grateful if. . .

如蒙赐教,不胜感激.

Your kind answer will be highly appreciated.

如蒙同意,不胜感激.

Your compliance with our request will be highly appreciated.

如果您能…，我将不胜感激。

I would be most obliged if…

如果您能…，我将不胜感激。

I would be most obliged if . . .

如能及时答复，不胜感激。

Your prompt reply would be appreciated.

如能及时回复，将不胜感激。

Your prompt reply will be very much appreciated.

承蒙厚爱,不胜感激.

I am beholden to you for your kindness.