There's nothing stopping you from lying to a recruitment agent about how much your previous salary was. People do this all the time.
You are wrong. Recruitment agencies as well as some corporates use a verification company so if you lied about your salary or said you have a MSCE on your CV but in fact you don't then the report coming back will be concrete evidence that you will be caught out.
Also companies, i know ours do as well as the client i work at demand a valid payslip which also goes through a verification process so if i were you i wouldn't chance it. It is just not worth it.