If not along Poynders Road, it might be worth looking at the other routes the map suggests she might have taken.
The 51 minute route is -
Long Road (the A3), cutting through the other end of Clapham Common,
then Rookery Road,
then turning left on the A24 for a short distance and crossing over, to go down Crescent Lane,
(which would take her past the other end of Clarence Ave re. phone signal),
crossing over Kings Ave
continuing along Crescent Lane to Lyham Road,
crossing over to walk along Ramilles Close/Blenheim Gardens to Brixton Hill.
crossing over Brixton Hill and walking a short way along it before
turning left into Endymion Road, where the map trail ends.
There's cctv on Henry Twining Court, Crescent Lane, which could confirm this.
The 49 minute route (quickest route, shaving a minute off the Poynders Road route)
This looks like a cut-through of various housing estates, taking a myriad of short turnings and alleys (Trouville/Rodenhurst/other estate) to get across, almost running parallel behind Poynders Road for a short while,
cutting across Clarence Avenue (phone signal) to Clarence Crescent,
then a few roads (Fennings/Fairbourne/Allingham) to get to Kings Ave,
crossing over to Thorncliffe Rd,
then turning right into Kingswood Rd,
then taking Chale Road and Dumbarton Road to get to Brixton Hill.
There's cctv at Phambra Food Store on the end of Chale Road which could confirm this.
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I'm not sure why her friend mentions her "ride home". She was talking to her boyfriend for 15 minutes before her last phone signal at 9:28pm at Clarence Ave, which is walking speed.