Birthday parties may not always occur on, or even around, the actual day. But that's not to say you can't celebrate in the same manner you would if the party was held on or closer to the big day. You merely need to throw in some slight modifications to the wording in order to properly word an invitation to a belated birthday party.
Write the name of the person whose birthday you are celebrating and include their age. You do not need to go into any detail as to why the party was postponed unless you are celebrating something additional. Examples could be recovery from an illness or an accident or moving it closer to someone else's birthday to have a joint celebration.
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Write the date, time and location of the party. You want to be as specific as possible, especially if the date of the party is much later than the actual birthday. People will not be expecting to attend a party in June for a relative born in December.
Write any important details, such as if it will be a surprise party a theme party. You don't want your guests showing up dressed inappropriately or spilling the beans to the guest of the honor prior to party day.
Write the name, number and email of the person to whom the RSVP should go, as well as the deadline for receiving them. Email is especially helpful because you have the RSVPs in writing. If the party has been rescheduled, give a generous amount of time for people to respond--they may be skeptical as to whether it will actually take place.
Include any rain dates or potential location changes. This way you don't blindside your guest with unexpected changes right before the party.