This customer has asked that someone else from the company get in touch with him/her because he hasn't been able to contact A.
A hasn't gotten back to this customer, so he would like someone else to get back to her as soon as possible.
ーThis customer has asked that someone else from the company get in touch with him because he hasn't been able to contact A.
「このお客様はAさんと連絡が取れないので、会社の誰か他の人から連絡を取ってほしいそうです」
to get in touch with ... で「…に連絡する・連絡を取る」
to contact で「連絡を取る」
ーA hasn't gotten back to this customer, so he would like someone else to get back to him as soon as possible.
「Aさんはこのお客様にずっと連絡を取っていないので、誰か他の人にできるだけ早く連絡をしてほしいそうです」
hasn't gotten back to ... で「…にずっと折り返し連絡をしていない・返事をしていない」
as soon as possible で「できるだけ早く」
ご参考まで！
カナダ 
