thermoelectric generator
My question is can a thermoelectric generator(input:heat difference to output:electricity) module also work as a peltier module(Input: current to output:cooling effect)?


Usually yes - BUT it is a very good idea to consult the manufacturer's data and see what they say. A TEG is usually a better specified TEC - it is usually able to run at higher hot-side temperatures and may have more "cells" to allow a greater voltage for a given temperature differential.

TEGS are usually more expensive than TECS of similar ratings - you need to have a good reason to use a TEG as a TEC. 

You can use low cost Peltier coolers (TECs) as TEGs - with lower output and often lower efficiency than the apparently similar spec TEG. 

TEG "Carnot efficiency is (Thot-Tcold)/Thot in absolute degrees eg degrees Kelvin where 0 C ~+ 273 K. Actual efficiency will be a smallish fraction of Carnot efficincy but increases with increasing temperature differential.
Real world TEGs typically give 5%+ efficiency with Thot = 200C and Tcold at around 30 C. 

TEG = Thermoelectric Generator = Seebeck effect
TEC = Thermoelectric Cooler = Peltier effect



Wikipedia Thermoelectric effect

Seebeck effect - images linked to web pages