We know that a player can choose to give his inspiration to another player (PHB, p. 125, emphasis mine) :
[…] if you have inspiration, you can reward another player for good roleplaying, clever thinking, or simply doing something exciting in the game. When another player character does something that really contributes to the story in a fun and interesting way, you can give up your inspiration to give that character inspiration.
Yesterday, the group I'm DMing was in a tough fight and one character had to make a save vs a creature's breath. Another player, who had earned inspiration earlier due to good roleplaying decided to give him his inspiration, in order to grant him advantage on the saving throw.
I ruled that inspiration couldn't be awarded just because a player badly needs it, for that would open the door to abuse.
After a long argument, the players bent to my ruling, but I felt they weren't convinced at all.
Can a player really give his inspiration to another at any moment, even if the second player didn't earn the reward by doing something good, clever or exciting?
After consulting the entry about Inspiration in the DMG (p. 240-241), I still can't make up my mind. The section gives a lot of headroom for approaches and variants, but, in essence, it all comes down to the table following guidelines that have been agreed on collectively. In order to help the table set those guidelines, I need to know how important it is to earn inspiration by actively doing something.
Best Answer
Yes, The Player Can Give It Anytime.
The DM gives the resource to the player based on the DM's judgment of what is cool/fun/in character roleplay.
The player uses their judgment to determine when they think another player is worthy of their inspiration. If it required the DM to think it was also awesome, the DM would have just given the player inspiration on their own; but this is a way for the players to affect the story and build comradery. This choice is the player's choice alone.
The player passing their inspiration to the other player gets to make the ruling if the other player is doing good roleplayer, clever thinking, or simply something exciting in the game. If it is a crucial roll (a roll they need), it is something exciting happening in the game and the player should be able to pass the inspiration. If a DM should rule that whatever they passed it for wasn't clever enough, not good roleplaying, or not exciting enough because that undermines the whole mechanic.
Moreover, DM granted inspiration is a very limited resource in most games. Running roughshod over how your players choose to spend that resource disenfranchises your players and in a moment when the players are doing something you want them to do -- acting as a team.