how do i record a telephone conversation on a bt synergi 5500 cordless anse?

Doesn't look like you can wit hthat phone.

Here's the manual. Just search for the word "record". The only context it appearsis to record the outgoing message memos and recording an incoming call (answerphone)

You could try searching for stuff

I did find this but its pricey:

http://retellrecorders.co.uk/shop/

This may be more economical - dx.com are normally pretty good:

This one looks like it would record to an iternal SD Card

http://www.dx.com/p/bstuo-smart-call-recording-digital-voice-recorder-white-438519#.WHIQwlwWZ_k

This one looks like it needs to be connetced to a PC

http://www.dx.com/p/jb-usb1-multi-model-1-channel-usb-telephone-recorder-black-203778#.WHIQy1wWZ_k

HTH
January 2017