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If Liked Songs are not syncing between your devices, it's best you reinstall both of your apps following this guide. This can sometimes occur if the is broke app cache on one of your devices.
Another reason for this could be a VPN or a work/ school network, which is blocking networking traffic. You can try connecting both your phone and PC to a different network and check if the Liked Songs are still out of sync.
Keep us posted on how you get on with this.
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