Well yes, generally speaking, once you have uv mapped an object that mapping is generally recognized by most 3D programs. The difference sometimes is that different 3D software systems handle tiling differently. I take it that the image on the left is the model you relating to. In this case, the model may be uv mapped correctly but the picture tiling is off. Most programs allow you to alter this number. Parametric mapping is a 1x1 tiling of the picture image meaning that one complete tile image will cover the model properly but sometimes depending on what software package you use to map, you may need more than a 1x1 ratio. You may try 2x2, 3x3 and so on to attain the same results using a different package or the size of your image tile. In Texture editor go to "editor" button on the image texture and alter the scale control.