Big country, but unhelpfully for us, from the invading point of view, it doesn’t have a coastline and because of that, and assorted other quirks of history, we’ve not had that much to do with it militarily. If you know otherwise, let me know.
As far as I can work out, the closest we’ve got to invading Belarus is an assortment of English knights who led expeditions to fight alongside the Teutonic Knights in the fourteenth century. At the height of their power, the Teutonic Knights extended their control as far inland as Grodno in Belarus, so it’s possible some of our lot may have made it that far as well. Certainly some were active in besieging Vilnius (see Lithuania), which isn’t much more than 20 miles from the border with Belarus.
There were, however, in an interesting bit of history that deserves to be better known, a number of Scots playing a major role in Russian armies around the end of the seventeenth century and the beginning of the eighteenth century. About fifteen generals of Scottish origin were working with the Russians in this period and, generally speaking, the Scots seem to have played a more significant role than any other nation in Russian forces at this time. Some of them operated in what is now Belarus. Marshal Baron George Ogilvie, for instance, commanded an army in the Grodno region in this period. Grodno seems to have been relatively popular with armies.