The girl and the boy are in different countries.

Answer

A nikah is not valid if conducted by telephone. The validity of Nikah is reliant on the Ijaab and Qubool being pronounced verbally in the presence of two Muslim male witnesses at the same venue. The simple way of performing such a marriage is for the woman to appoint a representative in the town/city where the man is. He will represent her at the Nikah ceremony which will be performed as usual. Or the man can appoint someone to represent him in the place where the woman is. The representative will then attend the Nikah ceremony on his behalf. The appointment of representatives may be done telephonically.

Another method is to perform the Nikah by letter. One party can fax or e-mail a letter in which he/she proposes Nikah to the other spouse. This letter will be read out in the presence of witnesses, and the prospective spouse will verbally announce his acceptance