Warp a shapefile from transverse Mercator to Lambert projection

How do I change the projection of a shape file in QGIS?

In the Export screen, type in a new shapefile name and click on the three dots next to the File name box to select the folder. Under the CRS dropdown, select the Project CRS as the assigned CRS. Click on the OK button and your new shapefile will be exported into the designated CRS.
 

What is the difference between UTM and MTM?

MTM is like UTM, but more precise. The zones are 3° large instead of 6° for UTM. The scaleTM is 0.9999 instead of 0.9996. The false easting is 304.8 km (instead of 500km for UTM).
 

What is 3 degree modified transverse Mercator projection?

The MTM projection, which is also called a 3-degree Transverse Mercator (3TM) projection, may be considered as a densification of the UTM projection. In order to avoid negative coordinates, the true origin of the grid coordinates is shifted by introducing the false northing and false easting.