The sources gathered here are mostly about method of Torah study rather than about gilgulim: Even Sheleimah 8:1, Even Sheleimah 8:2, Even Sheleimah 8:3, and Even Sheleimah 8:4 discuss how one should learn — choosing an accessible and untainted craft or tractate, filling one's belly with Scripture, Mishnah, and Talmud before engaging in pilpul, and the difference between the wise student who delights in learning and the fool who rushes to finish — none of which touches the topic of gilgulim at all.]
Only two sources here actually engage gilgulim, and neither is attributed to the Gra as a systematic teaching: Beur HaGra on Yonah, Hakdama 1 states that the soul of Yonah was sent to the world to rectify it, and having instead further damaged itself, was sent into a second gilgul to complete that rectification, though in sorrow over its bad fortune.]
Separately, Sha'ar HaGilgulim lays out the general mechanism of gilgul — that one who did not complete his rectification in a first incarnation must return in a second to finish it, illustrated by the case of Bava ben Buta returning as Rav Sheshet — but this passage is not framed as the Gra's own statement.]
Taken together, the sources on this sheet do not cohere into a Gra-specific account of gilgulim: the bulk of the set (Even Sheleimah 8:1, Even Sheleimah 8:2, Even Sheleimah 8:3, Even Sheleimah 8:4) addresses an unrelated subject, and the one passage tied to the Gra by name (Beur HaGra on Yonah, Hakdama 1) speaks only to Yonah's own case rather than a general doctrine of gilgulim.]