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Massive blunders

Ah, I had tried that but it didn't work. Turns out it was my mobile browser not cooperating :)

If I had to guess, your GUI in that replay mode is likely just sending Stockfish the FEN of each position in the game, instead of sending it the game.

You could confirm if you enabled the SF UCI option "Write Debug Log".

If I'm right, you'd see in that log file (defaults to io_log) in the same folder as the executable) a bunch of commands like the following:

position fen 1b2bB1/pp1kp1pp/8/4N3/3n3n/8/PPPK1PPP/R1B4R b - - 4 18

Arena and most other GUIs when playing through a game actually send the entire game, so for that same position, those GUIs when they have the full PGN will send this command:

position startpos moves e2e4 f7f6 d2d4 b8c6 g1f3 d7d6 b1c3 g8h6 e4e5 d6e5 d4e5 f6e5 d1d8 c6d8 f3e5 d8e6 f1c4 e6d4 e1d2 h6f5 c3d5 e8d8 e5f7 d8e8 d5c7 e8d7 c7a8 h8g8 f7e5 d7d8 c4g8 f5h4 e5f7 d8d7 f7e5

Both get you analysis of the same position, but only the second allows Stockfish to see that the position has already occurred once before.

Your GUI sending just the FENs is almost certainly what is happening. Whether you want to find out with the debug log is up to you :)
Thanks for explanation. I'll try with Arena, but anyway your point seems to be quite reasonable.
Just tried with Arena. You're right. Thanks again.
(I mean that the eval goes to +13 or 14, Arena always evaluates from the perspective of the player in turn, hence the inverted sign in my post above)

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