Before a new shell is made, the amoeba collects building material in its environment. In this case Difflugia lobostoma uses small mineral grains, in other words: minute sand grains.
Amoebae can also use diatom shells or fragments, and mix it with mineral grains. Some amoeba secrete their own building material, called idiosomes, like granules (Arcella), squared plates (e.g. Quadrulella) or circular ones (e.g. Trinema, Cyphoderia). Other species strip the plates from the shells of their prey. In Nebela-species one can often see where the plates are derived from.
When the new shell is build, the amoeba uses its own cytoplasm as a matrix for the new shell. It secretes an organic cement and the mineral grains are arranged all over the matrix, often in a very regular and symmetric way. The organic cement hardens and holds the embedded material together.
The formation of a new shell can be completed within half an hour! See here for another division.