transferring shares help

My ex (de-facto) and I converted what HDR shares we could to TLW shares in Jan 07. Since then we have split up and the shares are in both our names. I want to continue to hold the Tullow shares and he has agreed to transfer them into my name(once a $ amount has been agreed). Can anyone assist with who I should seek advice from regarding tax liability in this instance?? I'm quite confused.

Thanks in advance for any replies.