"传真电话业务" can be translated as "facsimile (fax) telephony service" or simply "fax service" in English, depending on the context and level of specificity required.
"Facsimile (fax) telephony service" emphasizes the integration of fax and telephony functions, which might be more precise in a technical or telecommunications context.
"Fax service" is a more general and commonly used term, especially when referring to the provision of fax capabilities as part of a broader communication service.