The funeral of PC Fiona Bone has taken place at Manchester Cathedral.
The 32-year-old constable died in a gun and grenade attack alongside colleague PC Nicola Hughes, 23, in Mottram, Greater Manchester, last month.
On its website the LGF also said: “We must remember that there are many serving lesbian, gay and bisexual police staff who play a crucial role in serving their local communities and we would like to honour them.
“Our thoughts are with everyone at GMP and serving police officers everywhere.
“We are indebted to their bravery and they deserve our respect and support.”
The funeral cortege passed through the city centre from the junction of Deansgate and Quay Street to Manchester Cathedral.
Officers from Greater Manchester Police and those who have travelled to help from forces all over the country lined the streets.
PC Bone’s family were led into the cathedral by her partner’s five-year-old daughter as a piper played the bagpipes.
Chief Constable Sir Peter Fahy said PCs Hughes and Bone “exemplified the very best of British policing”.
The Police Federation has begun selling wristbands in honour of the officers, with all money raised to be donated to their families.
Dale Cregan, 29, is in custody charged with the officers’ murders, along with those of two other men.