Does our heavenly Father forgive but not forget our sins against HIM? Does he temporarily give us a "pass" on our many transgressions only to later remind us of them? Even if He states that he will not remember our sins no more can he still recall them at any time?
The scriptures are clear concerning what it means for God to forgive the transgressions of sinners who repent. He has promised to be merciful and never recall our disobedience ever again and to permanently forgive us.
For I will be merciful toward their unrighteousnesses, and their sins and their lawlessness I will not remember ever again (Hebrews 8:12, HBFV throughout)
The Lord has, and will continue to be, merciful and gracious to us, and will bestow on us an abundance of mercy. Ultimately, he will not deal with us according to what our sins deserve, but to those who repent and overcome, he will forgive and forget all their trangressions as far as the east in from the west (see Psalm 103:8, 10 - 12).
God means exactly He says! His love for us, through the sacrifice of Jesus (John 1:29, etc.), is perfect and complete. If we sincerely pray to him and repent, through and in the name of Jesus Christ who became sin for us (Isaiah 53:4 - 6, 10 - 11), he promises to forgive.
How awesome is his love in this regard? Let us say that ten minutes after we ask God, in prayer, to forgive us of certain sins (which he does) we bring back up those same sins. What would be God's answer? No doubt, it would be something like 'Sins? I do not remember any sins that you committed!'
How to treat others
It is simple. Since God will forgive and totally forget our many sins, we can and should do the same for the sin or two our fellow humans commit against us. Even Jesus, in great physical pain after being tortured and nailed to the cross, still found reasons to request those who were killing him be pardoned of their transgressions (Luke 23:33 - 34).
There is yet something more amazing. Our Father in heaven promises there will come a time when He will decide never to remember our forgiven sins into the ages of eternity! It will be a time when the truth will be accessible and known by everyone and the point from which God will decide to NEVER, ever recall any of the sins each of us have committed against him (Jeremiah 31:34).
How serious should we take God's command that we forgive, in our hearts, the sins of OTHERS as he does for us? Jesus, in what is known in the Bible as the Sermon on the Mount, made it plain what God expects of us and told us what the consequences for not obeying him are.
If we refuse to overlook and forget what others have done to us then He will not pardon our disobedience against him! But, if we are willing to forgive others of what ultimately amount to little things, then God is more than happy to do the same for us over big things (Matthew 6:14 - 15).
We do not truly forgive, as God wants us to, unless we also forget.