My new HP laptop and my old Huawei smartphone have been paired, but every time I try to connect them via Bluetooth, it says connected for a second or two before connection fails. Both devices are easily connected with my Bluetooth headset. Any ideas on how to solve this problem? 

1- Have you removed the BT pairing between them and paired them again?

 

2- Is your Laptop fully up to date?

 

Agreed with the post above. Forget the bluetooth connection and re-pair see if it fixes it. Maybe uninstall/restart/update driver. Also if you're using windows, in device manager under the power settings tab of your bluetooth device "Allow the computer to turn off this device to save power" is notorious for causing issues like this.

 

Luckily if you're just trying to transfer files between the two there's a ton of other solutions that don't involve bluetooth if you'd rather not bother with it. From user-friendly cloud or direct transfer app based solutions (I'd recommend KDE connect) to a bit more complicated like SSH or FTP all the way to just plugging in a USB cable.