$\DeclareMathOperator\SL{SL}$The stable real cohomology of $\SL_n(\mathbb Z)$ was computed by Borel: it is given by $\mathbb R[z_i\mid i=5,9,13,\dotsc]$ with $z_i$ in degree $i$. One may wonder whether the pull back of the stable class $z_i$ on $\SL(\mathbb Z)$ to $\SL_n (\mathbb Z)$ for some finite $n$ is non-zero. That is, whether $\iota_n^* z_i = 0 \in H^i(\SL_n(\mathbb Z),\mathbb R)$ for $\iota_n \colon \SL_n(\mathbb Z) \to \SL(\mathbb Z)$.

Borel's proof also gives a real cohomological stability result and hence gives a range of $n$'s for which this is true, but in 1978 Ronnie Lee announced a proof in On unstable cohomology classes of $\SL_n(\mathbb Z)$ that $z_i$ is non-zero as long as $i<2n-3$, a much larger range of $n$'s than what can be deduced from Borel's proof. His paper says

Because the proofs of Theorems 1 and 2 require careful geometric construction, it is planned to present the detailed proof later, and we will indicate here some of the ideas involved in the case when $n$ is odd.

but as far as I know no detailed proof has appeared. My questions are: Has any proof of Ronnie Lee's theorem appeared in the literature? If not, what is the best known range for non-vanishing of the stable Borel classes?