I apologize for this type of question, but I'm having some trouble to understand remark 3.4(4) on page 212 of this article, that reads

The restriction of $\overline{\mathcal{G}}$ (the foliation aproaching $\overline{\mathcal{F}}$ obtained in Theorem 3.3) to the closure of a leaf of $\overline{\mathcal{F}}$ is defined by a fibration over the torus $\mathbb{T}^n$, and the group structure of this torus is well-defined.

The author indicates Lemma 3.2 as the justification, but I do not see how it follows, as that lemma only applies to the 1-forms $\alpha_i$ that define $\overline{\mathcal{F}}$, and not (necessarily) to the harmonic 1-forms $u_i$ that he uses, in the proof of Theorem 3.3, to perturbate $\alpha_i$ and get $\overline{\mathcal{G}}$.

I wonder if it's perhaps a misprint and the justification is actually Lemma 3.1, the torus appearing as the quotient of $\mathbb{R}^n$ (as he shows that, restricted to a closure $N$ of a leaf, $\overline{\mathcal{F}}$ is a Lie $\mathbb{R}^n$-foliation) by the holonomy representation $H(\pi_1(N))$, but I think in the end this would be equivalent to affirm that Lemma 3.2 also holds for the $u_i$s.

Note that this remark is used in the proof of Theorem 3.5.

I'd appreciate any insight on that matter.