Your wife is the applicant and strictly speaking needs to be involved in the process. This letter is a direct communication to the ECM. It is not a formal or official route and as I said before, the ECM/ECO is not obliged to review it. Please have your wife sign the letter.
Also please do not forget that the appeal must be done within time constraints.
Did your wife already receive the UKBA appeals documents and instructions?
In my posting I mentioned consideration be given to utilising the services of a professional. Only you can be the judge of that after you have balanced the grounds for refusal with the submitted application. If it's clearly an error on the part of the ECO then you could manage without engaging a professional. There are lots of experienced and willing helpers here in the forum.
Just my personal opinion, but I very much doubt that a local lawyer/advisor in Phils has the experience, caselaw or immigration knowledge to be able to handle this for you. I could be totally wrong but it's my feeling and I felt I needed to explain that.
Use all the members on this forum. It's the range and diversity of knowledge that make it so great.