I think the stone-built chair-shelter that replaced the matshed shelter is shown here, so the date should be mid 1901 or a bit later.
Source: This image came from Flickr, see https://flickr.com/photo.gne?id=11903638985
Date picture taken
1 Jul 1901
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Postbox at Victoria Gap
I think in front of the Upper Terminus of the Peak Tram and beside the steps leading up to the Peak Hotel is the postbox at Victoria Gap. The pillar box may have been temporarily relocated there whilst the stone chair shelter was being constructed.
Re Postbox at Victoria Gap
Very well spotted! This likely is the postbox. The original place of the postbox was on the left side of Mount Austin Road (see early photos). When Harlech Road was constructed (opened in 1904), it had to be relocated. Possibly the position you spotted was also not used very long, it certainly had to be relocated again when the Peak Hotel Garage was constructed.